1. Solve P = 2L + 2W for L 2. Solve A = 1/2 bh for h Quiz 1. Solve P = 2L + 2W for L 2. Solve A = 1/2 bh for h 3. A chemist must mix 8 L of a 40% solution with 70% solution to get a 50% solution. How much of the 70% solution should be used?
Ten liters of a 4% acid solution must be mixed with a 10% solution to get a 6% solution. How many liters of the 10% solution are needed?
Slope of a Line
Slope An important characteristic of a straight line is its slope, a numerical measure of the steepness of the line. (Geometrically, this may be interpreted as the ratio of rise to run.
Find the slope of the line through each of the following pairs of points. y x
Find the slope of the line through each of the following pairs of points. y x
Find the slope of the line through each of the following pairs of points. y x
Find the slope of the line through each of the following pairs of points. y x
Find the slope of the line through each of the following pairs of points. y x
Find the slope of the line through each of the following pairs of points. y x
Find the slope of the line through each of the following pairs of points. y x
Find the slope of the line through each of the following pairs of points. y x
Find the slope of the line through each of the following pairs of points. y x
Find the slope of the line through each of the following pairs of points. y x
Find the slope of the line through each of the following pairs of points. y x
Find the slope of the line through each of the following pairs of points. y x
Find the slope of the line through each of the following pairs of points. y x
Find the slope of the line through each of the following pairs of points. y x
Find the slope of the line through each of the following pairs of points. y x
Find the slope of the line through each of the following pairs of points. y x
Find the slope of the line through each of the following pairs of points. y x
Find the slope of the line through each of the following pairs of points. y x
Find the slope of the line through each of the following pairs of points. y x
Find the slope of the line through each of the following pairs of points. y x
Find the slope of the line through each of the following pairs of points. y x
Find the slope of the line through each of the following pairs of points. y x
Find the slope of the line through each of the following pairs of points. y x
Find the slope of the line through each of the following pairs of points. y x
Find the slope of the line through each of the following pairs of points. y x
Find the slope of the line through each of the following pairs of points. y x
Find the slope of the line through each of the following pairs of points. y x
Find the slope of the line through each of the following pairs of points. y x
Find the slope of the line through each of the following pairs of points. y x
Find the slope of the line through each of the following pairs of points. y x
Find the slope of the line through each of the following pairs of points. y x
Find the slope of the line through each of the following pairs of points. y x
Find the slope of the line through each of the following pairs of points. y x
Find the slope of the line through each of the following pairs of points. y x
Find the slope of the line through each of the following pairs of points. y x
Find the slope of the line through each of the following pairs of points. y x
Find the slope of the line through each of the following pairs of points. y x
Find the slope of the line through each of the following pairs of points. y x
Find the slope of the line through each of the following pairs of points. y x
Find the slope of the line through each of the following pairs of points. y x
Find the slope of the line through each of the following pairs of points. y x
Find the slope of the line through each of the following pairs of points. y x
Find the slope of the line through each of the following pairs of points. y x
Find the slope of the line through each of the following pairs of points. y x
Find the slope of the line through each of the following pairs of points. y x
Find the slope of the line through each of the following pairs of points. y x
Find the slope of the line through each of the following pairs of points. y x
Find the slope of the line through each of the following pairs of points. y x
The difference x2-x1 is called the change in x The difference y2-y1 is called the change in y 8 6 (x2,y2) 4 (x1,y1) 2 (x2,y1) -2 2 4 6
Slope Using Coordinates The slope m of the line through the points (x1,y1) and (x2,y2) is
Slope Using Coordinates The slope m of the line through the points (x1,y1) and (x2,y2) is m = = rise y2 - y1 run x2 - x1
Slope Using Coordinates The slope m of the line through the points (x1,y1) and (x2,y2) is m = = rise y2 - y1 run x2 - x1 Note: when x2 - x1 = 0 then the line line is vertical and the slope is undefined
Find the slope of the line y x
Find the slope of the line y x
Find the slope of the line y x
Find the slope of the line y x
Find the slope of the line y x
Find the slope of the line y x
Find the slope of the line y x
Find the slope of the line y x
Find the slope of the line y x
Find the slope of the line y x
Find the slope of the line y x
Find the slope of the line y x
Find the slope of the line y x
Find the slope of the line y x
Find the slope of the line y x
Find the slope of the line y x
Find the slope of the line y x
Find the slope of the line y x
Find the slope of the line y x
Find the slope of the line y x
Find the slope of the line y x
Find the slope of the line y x
Find the slope of the line y x
Find the slope of the line y x
Find the slope of the line y x
Find the slope of the line y x
Find the slope of the line y x
Find the slope of the line y x
Find the slope of the line y x
Find the slope of the line y x
Find the slope of the line y x
Slope
The slope of a horizontal line is 0
The slope of a horizontal line is 0 The slope of a vertical line is undefined..
The slope of a horizontal line is 0 The slope of a vertical line is undefined. Do not say that a vertical line has no slope because “no slope” could be confused with 0 slope, which is the slope of a horizontal line.
Solve for y to find the slope of the line
Solve for y to find the slope of the line
Solve for y to find the slope of the line
Solve for y to find the slope of the line
Solve for y to find the slope of the line
Solve for y to find the slope of the line
Solve for y to find the slope of the line
Solve for y to find the slope of the line
Solve for y to find the slope of the line
Solve for y to find the slope of the line
Solve for y to find the slope of the line
Solve for y to find the slope of the line 4x - y = -8
4x - y = -8 Standard Form Ax + By = C Solve for y to find the slope of the line 4x - y = -8 Standard Form Ax + By = C
4x - y = -8 Standard Form Ax + By = C Solve for y to find the slope of the line 4x - y = -8 Standard Form Ax + By = C
4x - y = -8 Standard Form Ax + By = C Slope Intercept Form Solve for y to find the slope of the line 4x - y = -8 Standard Form Ax + By = C Slope Intercept Form
4x - y = -8 Standard Form Ax + By = C Slope Intercept Form y = 4x + 8 Solve for y to find the slope of the line 4x - y = -8 Standard Form Ax + By = C Slope Intercept Form y = 4x + 8
4x - y = -8 Standard Form Ax + By = C Slope Intercept Form y = 4x + 8 Solve for y to find the slope of the line 4x - y = -8 Standard Form Ax + By = C Slope Intercept Form y = 4x + 8 y = mx + b
Find the slope of the line y x
Find the slope of the line y x
Find the slope of the line y x
Find the slope of the line y x
Find the slope of the line y x
Find the slope of the line y x
Find the slope of the line y x
Find the slope of the line y x
Find the slope of the line y x
Find the slope of the line y x
Find the slope of the line y x
Find the slope of the line y x
Find the slope of the line y x
Find the slope of the line y x
Find the slope of the line y x
Find the slope of the line y x
Find the slope of the line y x
Find the slope of the line y x
Find the slope of the line y x
Find the slope of the line y x
Find the slope of the line y x
Find the slope of the line
Find the slope of the line
Find the slope of the line
Find the slope of the line
Find the slope of the line
Find the slope of the line
Find the slope of the line
Find the slope of the line
Find the slope of the line
Find the slope of the line
Find the slope of the line
Find the slope of the line
Find the slope of the line
Find the slope of the line
Find the slope of the line
Find the slope of the line
Find the slope of the line
Find the slope of the line
Find the slope of the line
Find the slope of the line
Find the slope of the line
Find the slope of the line
Find the slope of the line
Find the slope of the line
Find the slope of the line
Graph the line with slope 2/3 passing through the point (-1,4) y x
Graph the line with slope 2/3 passing through the point (-1,4) y x
Graph the line with slope 2/3 passing through the point (-1,4) y x
Graph the line with slope 2/3 passing through the point (-1,4) y x
Graph the line with slope 2/3 passing through the point (-1,4) y x
Graph the line with slope 2/3 passing through the point (-1,4) y x
Graph the line with slope 2/3 passing through the point (-1,4) y x
Graph the line with slope 2/3 passing through the point (-1,4) y x
Graph the line with slope 2/3 passing through the point (-1,4) y x
Graph the line with slope 2/3 passing through the point (-1,4) y x
Graph the line with slope 2/3 passing through the point (-1,4) y x
Graph the line with slope 2/3 passing through the point (-1,4) y x
Graph the line with slope 2/3 passing through the point (-1,4) y x
Graph the line with slope 2/3 passing through the point (-1,4) y x
Graph the line with slope 2/3 passing through the point (-1,4) y x
Graph the line with slope 2/3 passing through the point (-1,4) y x
Graph the line with slope 2/3 passing through the point (-1,4) y x
Graph the line with slope -4 passing through y the point (3,1) x
Graph the line with slope -4 passing through y the point (3,1) x
Graph the line with slope -4 passing through y the point (3,1) x
Graph the line with slope -4 passing through y the point (3,1) x
Graph the line with slope -4 passing through y the point (3,1) x
Graph the line with slope -4 passing through y the point (3,1) x
Graph the line with slope -4 passing through y the point (3,1) x
Graph the line with slope -4 passing through y the point (3,1) x
Graph the line with slope -4 passing through y the point (3,1) x
Graph the line with slope -4 passing through y the point (3,1) x
Graph the line with slope -4 passing through y the point (3,1) x
Graph the line with slope -4 passing through y the point (3,1) x
Graph the line with slope -4 passing through y the point (3,1) x
Graph the line with slope -4 passing through y the point (3,1) x
Graph the line with slope -4 passing through y the point (3,1) x
Graph the line with slope -4 passing through y the point (3,1) x
Graph the line with slope -4 passing through y the point (3,1) x
Graph the line with slope -4 passing through y the point (3,1) x
Graph the line with slope -4 passing through y the point (3,1) x
Lines that have positive slope point upward with the right hand.
Lines that have negative slope point upward with the left hand.
Two lines with slopes m1 and m2 are parallel if and only if Parallel lines Two lines with slopes m1 and m2 are parallel if and only if
Line l goes through the origin and is parallel to the line through (-2,-3) and (5,-5). Find the slope of line l.
Line l goes through the origin and is parallel to the line through (-2,-3) and (5,-5). Find the slope of line l.
Line l goes through the origin and is parallel to the line through (-2,-3) and (5,-5). Find the slope of line l.
Line l goes through the origin and is parallel to the line through (-2,-3) and (5,-5). Find the slope of line l.
Line l goes through the origin and is parallel to the line through (-2,-3) and (5,-5). Find the slope of line l.
Line l goes through the origin and is parallel to the line through (-2,-3) and (5,-5). Find the slope of line l.
Line l goes through the origin and is parallel to the line through (-2,-3) and (5,-5). Find the slope of line l.
Line l goes through the origin and is parallel to the line through (-2,-3) and (5,-5). Find the slope of line l.
Line l goes through the origin and is parallel to the line through (-2,-3) and (5,-5). Find the slope of line l.
Line l goes through the origin and is parallel to the line through (-2,-3) and (5,-5). Find the slope of line l.
Line l goes through the origin and is parallel to the line through (-2,-3) and (5,-5). Find the slope of line l.
(-2,-3) & (5,-5) y x
(-2,-3) & (5,-5) y x
(-2,-3) & (5,-5) y x
(-2,-3) & (5,-5) y x
(-2,-3) & (5,-5) y through the origin x
(-2,-3) & (5,-5) y through the origin x
(-2,-3) & (5,-5) y through the origin x
(-2,-3) & (5,-5) y through the origin x
(-2,-3) & (5,-5) y through the origin x
(-2,-3) & (5,-5) y through the origin x
(-2,-3) & (5,-5) y through the origin x
(-2,-3) & (5,-5) y through the origin x
(-2,-3) & (5,-5) y through the origin x
(-2,-3) & (5,-5) y through the origin x
(-2,-3) & (5,-5) y through the origin x
(-2,-3) & (5,-5) y through the origin x
y One line has a slope of 2 Perpendicular lines x
y One line has a slope of 2 Perpendicular lines x
One line has a slope of 2 and the other line has a slope of -1/2 y One line has a slope of 2 and the other line has a slope of -1/2 Perpendicular lines x
One line has a slope of 2 and the other line has a slope of -1/2 y One line has a slope of 2 and the other line has a slope of -1/2 Perpendicular lines x
One line has a slope of 2 and the other line has a slope of -1/2 y One line has a slope of 2 and the other line has a slope of -1/2 Perpendicular lines x
Two lines with slopes m1 and m2 are perpendicular if and only if Perpendicular lines Two lines with slopes m1 and m2 are perpendicular if and only if
Line l contains the point (1,6) and is perpendicular to the line through (-4,1) and (3,2). Find the slope of line l.
Line l contains the point (1,6) and is perpendicular to the line through (-4,1) and (3,2). Find the slope of line l.
Line l contains the point (1,6) and is perpendicular to the line through (-4,1) and (3,2). Find the slope of line l.
Line l contains the point (1,6) and is perpendicular to the line through (-4,1) and (3,2). Find the slope of line l.
Line l contains the point (1,6) and is perpendicular to the line through (-4,1) and (3,2). Find the slope of line l.
Line l contains the point (1,6) and is perpendicular to the line through (-4,1) and (3,2). Find the slope of line l.
Line l contains the point (1,6) and is perpendicular to the line through (-4,1) and (3,2). Find the slope of line l.
Line l contains the point (1,6) and is perpendicular to the line through (-4,1) and (3,2). Find the slope of line l.
Line l contains the point (1,6) and is perpendicular to the line through (-4,1) and (3,2). Find the slope of line l.
Line l contains the point (1,6) and is perpendicular to the line through (-4,1) and (3,2). Find the slope of line l.
Line l contains the point (1,6) and is perpendicular to the line through (-4,1) and (3,2). Find the slope of line l.
Line l contains the point (1,6) and is perpendicular to the line through (-4,1) and (3,2). Find the slope of line l.
(-4,1) and (3,2) y x
(-4,1) and (3,2) y x
(-4,1) and (3,2) y x
(-4,1) and (3,2) y x
(-4,1) and (3,2) y x
(-4,1) and (3,2) y x
(-4,1) and (3,2) y x
(-4,1) and (3,2) y x
(-4,1) and (3,2) y x
(-4,1) and (3,2) y x
(-4,1) and (3,2) y x
(-4,1) and (3,2) y x
(-4,1) and (3,2) y x
(-4,1) and (3,2) y x
(-4,1) and (3,2) y x
(-4,1) and (3,2) y x
(-4,1) and (3,2) y x
(-4,1) and (3,2) y x
(-4,1) and (3,2) y x
(-4,1) and (3,2) y x
(-4,1) and (3,2) y x
(-4,1) and (3,2) y x
(-4,1) and (3,2) y x
(-4,1) and (3,2) y x
Determine whether two lines are parallel or perpendicular
Determine whether two lines are parallel or perpendicular
Determine whether two lines are parallel or perpendicular
Determine whether two lines are parallel or perpendicular
Determine whether two lines are parallel or perpendicular
Determine whether two lines are parallel or perpendicular
Determine whether two lines are parallel or perpendicular
Determine whether two lines are parallel or perpendicular
Determine whether two lines are parallel or perpendicular
Determine whether two lines are parallel or perpendicular
Determine whether two lines are parallel or perpendicular
Determine whether two lines are parallel or perpendicular
Determine whether two lines are parallel or perpendicular
Determine whether two lines are parallel or perpendicular
Determine whether two lines are parallel or perpendicular
Determine whether two lines are parallel or perpendicular
Determine whether two lines are parallel or perpendicular
Determine whether two lines are parallel or perpendicular
Determine whether two lines are parallel or perpendicular
Determine whether two lines are parallel or perpendicular
Determine whether two lines are parallel or perpendicular
Determine whether two lines are parallel or perpendicular
Determine whether two lines are parallel or perpendicular
Determine whether two lines are parallel or perpendicular
Determine whether two lines are parallel or perpendicular
Determine whether two lines are parallel or perpendicular
Determine whether two lines are parallel or perpendicular
Determine whether two lines are parallel or perpendicular
Determine whether two lines are parallel or perpendicular
Determine whether two lines are parallel or perpendicular
Determine whether two lines are parallel or perpendicular
Determine whether two lines are parallel or perpendicular
Determine whether two lines are parallel or perpendicular
Determine whether two lines are parallel or perpendicular
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