Lesson 2.4 Quick Graphs of Linear Equations

1. Lesson 2.4 Quick Graphs of Linear Equations

2. Keywords: y-intercept x-intercept Slope-intercept form Standard form of a linear equation

4. GOAL: Use slope-intercept form and standard form to graph equations.

5. 3 – y x 2. = SOLUTION 4 Write the equation in slope-intercept form by adding to each side: STEP 1 3 x 4 3 ( ). 0, 2 + y x 2. = 4 Find the y-intercept. Comparing to , you can see that b2. Plot a point at STEP 2 3 + y x 2 = 4 + y mx b = = Example 1 Use Slope-Intercept Form to Graph a Line Graph

7. STEP 3 3 m = 4 ( ) 0, 2 ( ) 4, 5 STEP 4 Draw a line through the two points. 3 rise = run 4 Example 1 Use Slope-Intercept Form to Graph a Line Find the slope. The slope is , so . From , move up 3 units and right 4 units. Plot a Second point at .

8. Checkpoint 1. ANSWER 1 y x = 2 Use Slope-Intercept Form to Graph a Line Graph the equation.

9. Checkpoint ANSWER – – 2 y x = Use Slope-Intercept Form to Graph a Line Graph the equation. 2.

10. Checkpoint ANSWER 2 – y 3 x = 3 Use Slope-Intercept Form to Graph a Line Graph the equation. 3.

12. Example 2 ( ) 2 0 Graph . 3x + 2y 12 SOLUTION = Method 1 Use Standard Form 3x + 12 Let . y 0 = = x 4 Solve for x. = Draw Quick Graphs STEP 1 The equation is already written in standard form. STEP 2 Find the x-intercept. The x-intercept is 4, so plot the point (4, 0).

13. Example 2 ( ) 3 0 + 2y 12 = y 6 Solve for y. = Let . STEP 4 Draw a line through the intercepts. x 0 = Draw Quick Graphs STEP 3 Find the y-intercept. The y-intercept is 6, so plot the point (0, 6).

14. Example 2 + 2y 12 3x = 2y + 12 – Solve for y. 3x = Standard form 3 x 2 y + 6 – Slope-intercept form = Now graph using the method of Example 1. Draw Quick Graphs Method 2 Use Slope-Intercept Form Solve for y to rewrite the equation

15. Checkpoint ANSWER y + 3 – = 4. x + y 7 = 1 x 2 ANSWER 5. Draw Quick Graphs Graph the equation. Choose either method.

16. Checkpoint 5x + 2y 10 ANSWER = 6. Draw Quick Graphs Graph the equation. Choose either method.

18. Example 3 y + 4 = 3x y + 4. = 3x c. Graph the line that is perpendicular to the graph of at its y-intercept. y + 4 = 3x SOLUTION a. Draw the graph of using the y-intercept 4 and slope 3. y + 4 = 3x – ( 0, 1 ) Graph Parallel and Perpendicular Lines a. . Draw the graph of b. Graph the line that passes through and is parallel to the graph of

19. Example 3 y + 4 = 3x ( ) 0, 4 ( ) 3, 3 The slope of any line perpendicular to the graph of is the negative reciprocal of 3, or . So, from move down 1 unit and right 3 units. Plot a second point at . Draw the line. c. – ( ). 0, 1 1 – – ( ), y 0,1 + 4 = 3x 3 ( ) 1, 2 Graph Parallel and Perpendicular Lines b. Graph the point Any line parallel to the graph of has the same slope, 3. From move up 3 units and right 1 unit. Plot a second point at . Draw a line through the two points.

20. Checkpoint y – 2x 1 = ANSWER Graph Parallel and Perpendicular Lines Graph the line. On the same grid, graph (a) the line passing through the origin that is parallel to the original line, and (b) the line perpendicular to the original line at its y-intercept. 7.

21. Checkpoint ANSWER Graph Parallel and Perpendicular Lines Graph the line. On the same grid, graph (a) the line passing through the origin that is parallel to the original line, and (b) the line perpendicular to the original line at its y-intercept. 3 y x + 2 8. = 4

22. Checkpoint 1 – x + 1 y 9. = 5 ANSWER Graph Parallel and Perpendicular Lines Graph the line. On the same grid, graph (a) the line passing through the origin that is parallel to the original line, and (b) the line perpendicular to the original line at its y-intercept.

24. Slip

25. Homework