1. Graphing Linear Functions 1. graph linear functions. 2. write equations in standard form.

2. Warm Up, Do Now! Solve for y 1.3 – y = 10 2.2y + 4 = 8 3.9y + (-1) = 8 4.0 – 5 = -10y

3. Practice 1) Solve for y: 2x + y = 4 2) Solve for y: 4x + 2y = -6 3) Solve for y: x – 3y = 6 Solve for y means isolate y. Get y all by itself!

4. 1) Review: Solve for y 2x + y = 4 1.Draw “the river” 2.Subtract 2x from both sides - 2x - 2x y = -2x + 4 2) Solve for y: 4x + 2y = -6 1.Subtract 4x 2.Simplify 3.Divide both sides by 2 4.Simplify - 4x - 4x 2y = -4x - 6 2 2 y = -2x - 3

5. 3) Solve for y: x - 3y = 6 1.Subtract x 2.Simplify 3.Divide both sides by -3 4.Simplify - x - x -3y = -x + 6 -3 -3 or

6. Graphing Steps 1)Isolate the variable (solve for y). 2)Make a t-table. If the domain is not given, pick your own values. 3)Plot the points on a graph. 4)Connect the points.

7. Make a t-table If f(x) = 2x + 4, complete a table using the domain {-2, -1, 0, 1, 2}. 2(-2) + 4 = 0(-2, 0) 2(-1) + 4 = 2(-1, 2) 2(0) + 4 = 4(0, 4) 2(1) + 4 = 6(1, 6) 2(2) + 4 = 8(2, 8) xf(x) -2 0 1 2 ordered pair

8. 1) Given the domain {-2, -1, 0, 1, 2}, graph 3x + y = 6 -3(-2) + 6 = 12(-2, 12) -3(-1) + 6 = 9 (-1, 9) -3(0) + 6 = 6 (0, 6) -3(1) + 6 = 3 (1, 3) -3(2) + 6 = 0 (2, 0) x-3x + 6 ordered pair 1.Solve for y: 3x + y = 6 Subtract 3x - 3x - 3x y = -3x + 6 2. Make a table -2 0 1 2

9. Bonus questions! What is the x-intercept? (2, 0) What is the y-intercept? (0, 6) Does the line increase or decrease? Decrease 1) Given the domain {-2, -1, 0, 1, 2}, graph 3x + y = 6 3.Plot the points (-2,12), (-1,9), (0,6), (1,3), (2,0) 4.Connect the points.

10. 1.. 2.. 3.. 4.. Ex.2) Which is the graph of y = x – 4?

11. Standard Form Ax + By = C A, B, and C have to be integers An equation is LINEAR (the graph is a straight line) if it can be written in standard form.

12. Determine whether each equation is a linear equation. 3) 4x = 7 + 2y Can you write this in the form Ax + By = C? 4x - 2y = 7 A = 4, B = -2, C = 7 This is linear!

13. 4) 2x 2 - y = 7 Can you write it in standard form? NO - it has an exponent! Not linear 5) x = 12 x + 0y = 12 A = 1, B = 0, C = 12 Linear Determine whether each equation is a linear equation.

14. Here’s the cheat sheet! An equation that is linear does NOT contain the following: 1.Variables in the denominator 2.Variables with exponents 3.Variables multiplied with other variables. xy = 12

15. Is this equation linear? 1.Yes 2.No Standard Form x – 4y = 3

16. Is this equation linear? 1.Yes 2.No Exponents are not allowed!

17. Is this equation linear? y = -3 1.Yes 2.No Standard Form 0x + y = -3

18. x and y -intercepts ● The x-intercept is the point where a line crosses the x-axis. The general form of the x-intercept is (x, 0). The y-coordinate will always be zero. ● The y-intercept is the point where a line crosses the y-axis. The general form of the y-intercept is (0, y). The x-coordinate will always be zero.

19. To find intercepts…. ●T●T o find the x-intercept, plug in 0 for y. ●T●T o find the y-intercept, plug in 0 for x.

20. Find the x and y- intercepts of x = 4y – 5 ● x-intercept: ● Plug in y = 0 x = 4y - 5 x = 4(0) - 5 x = 0 - 5 x = -5 ● (-5, 0) is the x-intercept ● y-intercept: ● Plug in x = 0 x = 4y - 5 0 = 4y - 5 5 = 4y = y ● (0, ) is the y-intercept

21. Find the x and y-intercepts of g(x) = -3x – 1* ● x-intercept ● Plug in y = 0 g(x) = -3x - 1 0 = -3x - 1 1 = -3x = x ● (, 0) is the x-intercept ● y-intercept ● Plug in x = 0 g(x) = -3(0) - 1 g(x) = 0 - 1 g(x) = -1 ● (0, -1) is the y-intercept *g(x) is the same as y

22. Find the x and y-intercepts of 6x - 3y =-18 ● x-intercept ● Plug in y = 0 6x - 3y = -18 6x -3(0) = -18 6x - 0 = -18 6x = -18 x = -3 ● (-3, 0) is the x-intercept ● y-intercept ● Plug in x = 0 6x -3y = -18 6(0) -3y = -18 0 - 3y = -18 -3y = -18 y = 6 ● (0, 6) is the y-intercept

23. Find the x and y-intercepts of x = 3 ● y-intercept ● A vertical line never crosses the y-axis. ● There is no y-intercept. ● x-intercept ● Plug in y = 0. There is no y. Why? ● x = 3 is a vertical line so x always equals 3. ● (3, 0) is the x-intercept. x y

24. Find the x and y-intercepts of y = -2 ● x-intercept ● Plug in y = 0. y cannot = 0 because y = -2. ● y = -2 is a horizontal line so it never crosses the x-axis. ● There is no x-intercept. ● y-intercept ● y = -2 is a horizontal line so y always equals -2. ● (0,-2) is the y-intercept. x y

25. Graphing Equations ● Example: Graph the equation -5x + y = 2 Solve for y first. -5x + y = 2Add 5x to both sides y = 5x + 2 ● The equation y = 5x + 2 is in slope-intercept form, y = mx+b. The y-intercept is 2 and the slope is 5. Graph the line on the coordinate plane.

26. x y Graph y = 5x + 2 Graphing Equations

27. Graph 4x - 3y = 12 ● Solve for y first 4x - 3y =12Subtract 4x from both sides -3y = -4x + 12 Divide by -3 y = x + Simplify y = x – 4 ● The equation y = x - 4 is in slope-intercept form, y=mx+b. The y -intercept is -4 and the slope is. Graph the line on the coordinate plane. Graphing Equations

28. Graph y = x - 4 x y Graphing Equations