Slope Graphing Writing Equations of lines Parallel and perpendiclar

Lines in the plane I. Slope Steepness of a line where x1 ≠ x2, that would be a vertical line

If the denominator of the slope is 0 then the slope is undefined and you have a vertical line +slope - slope 0 slope no slope A line with a positive slope rises from left to right A line with a negative slope falls from left to right A line with a slope of zero is horizontal A line with an undefined slope is vertical

Examples: Find the slope of the line passing through 1 Examples: Find the slope of the line passing through 1. (-2, -4) and (3, -1). 2. (3, -4), (1, 6) 3. (2, -1) , (2, 5)

4. Without graphing, tell whether the line through the given points rises, falls, is horizontal, or is vertical. ( 1, -2) , (3, -2)

5. Tell which line is steeper 5. Tell which line is steeper. Line 1: through (1, -4) and (5, 2) Line 2: through (-2, -5) and (1, -2)

6. Tell whether the lines through the given points are parallel, perpendicular, or neither. (1, -2), (3, -2) and (-5, 4), (0, 4) b) (-2, -2), (4, 1) and (-3, -3), (1, 5)

Slope-intercept form ~ y = mx + b II. Writing Linear Equations Slope-intercept form ~ y = mx + b Point-slope form ~ y – y1 = m (x – x1) Two points ~ m = y2 – y1 x2 – x1

Slope- Intercept y = mx + b. Slope- intercept form Slope- Intercept y = mx + b **Slope- intercept form ** m = slope b = y-intercept

Standard Form. Standard Form Standard Form ** Standard Form** Ax + By = C Where A and B are not both zero slope = y-int =

7. Write an equation of the line shown. 8. Write an equation of a line that passes through (-3, 4) and has a slope of .

9. Write an equation of a line that passes through (-2, -1) and (3, 4).

Write an equation of a line that passes through (2, -3) and is perpendicular to y = 2x + 3.

11. Write an equation of a line that passes through(2, -3) and is parallel to y = 2x + 3.

QUICK GRAPHS OF LINEAR EQUATIONS Terminology a) slope-intercept form b) standard form c) y-intercept = point where graph crosses the y-axis (let x = 0 and solve for y) d) x-intercept= point where graph crosses the x-axis (let y = 0 and solve for x)

To quick graph do the following: 1) Write equation in slope-intercept form 2) Find the y-intercept and plot the point 3) Find the slope and use it to plot a second point 4) Draw a line through the two points

Ex12.: Graph y =

To quick graph do the following: 1) Write equation in standard form 2) Find the y-intercept and plot the point 3) Find the slope and use it to plot a second point 4) Draw a line through the two points

Ex 13.: Graph 2x + 3y = 12

Graphing Horizontal and Vertical Lines a) horizontal lines are in the form: y = # b) vertical lines are in the form: x = #

14. Graph x = -2

15. Graph y = 5

To quick graph using a table do the following: 1) pick 3 x values 2) plug the x into the equation and solve for y 3) plot those points 4) Draw a line through the points

16. Graph y = -2x + 3 x y

To graph an inequality Graph the equation by the method of your choice Pick a point and check in the equation If it is true shade that direction If it is false shade the opposite side of the equation

17. Graph y < -2x + 3