2-3 Slope Slope indicates the steepness of a line. is “the change in y over the change in x” (vertical over horizontal). is the ‘m’ in y = mx + b.

Finding the Slope of a Line m = m We use the first equation when given a graph, the second when given a table, and the third when given two points.

Slope If a line rises from left to right (uphill), x y If a line rises from left to right (uphill), it has a positive slope. If a line falls from left to right (downhill), it has a negative slope. x y

Slope If a line is vertical, it has an undefined slope. If a line is horizontal it has a slope equal to 0. x y x y

Find the Slope To find the slope of this line we will use rise/run. Pick either point. We find the rise by counting up (+) or down (-). Rise is 3 up from the bottom or -3 down from the top point. y x

Find the Slope To find the run, we count right (+) or left (-). If you started from the top point, your run will be left -2, if you started at the bottom point, your run will be right 2. x y

Find the Slope So if you started with the top point, your x y So if you started with the top point, your slope would be -3/-2. If you started with the bottom point, your slope would be 3/2. Are these the same? Yes!! The slope of the line is 3/2.

Find the Slope x y x y m = m =

Find the Slope x y x y m= undefined m = 0

Find the Slope of the Line Given the points (5, 1) & (6, 4) m = = = 3 Given the points (-6, -2) & (-1, 0) m =

Slope-Intercept Form y = mx + b [or f(x) = mx + b] m is the slope b is the y-intercept

Find the Equation of the Line What is the y-intercept? b = -2 What is m? m = y = x -2 x y

Find the Equation of the Line b = ? b = 1 m = ? m = - y = - x + 1 x y

Find the Equation of the Line b = ? b = 4 m = ? m = 0 y = 0x+4 y=4 x y

Find the Equation Given the Slope and y-intercept 1) m = -3, b = 1 y = -3x + 1 2) m = - , b = -4 y = - x - 4

Find the Slope and y-intercept of each Equation: 1) y = -4x + 3 m = -4 b = 3 2) y = 5 - x m = - b = 5 3) 8x + y = m = -8 b = 4) 4x - 2y = 10 m = 2 b = -5

Find the Equation Given the Slope and a Point Given m = -1, (2, 1) First, calculate b by substituting the slope and the coordinates into y = mx + b. y = -1x + b 1 = -1(2) + b 1 = -2 + b 3 = b y = -1x + 3

Find the Equation Given Two Points Given (-1, 3) and (2, 1) First, calculate the slope: Second, find b. Use either point... m = , (2, 1) 1 = (2) + b 1 = + b = b

Homework: Graphing Linear Equations Worksheet (front and back)