1. 3.3 Graph Using Intercepts You will graph a linear equation using intercepts. Essential question: How do you use intercepts to graph equations? You will learn how to answer this question by finding and using the x – and y-intercepts of the graph of an equation.

2. Warm-Up Exercises Substitute 0 for y. Write original equation. To find the x- intercept, substitute 0 for y and solve for x. SOLUTION Find the x- intercept and the y- intercept of the graph of 2x + 7y = 28. Find the intercepts of the graph of an equation EXAMPLE 1 Solve for x. 2x + 7(0) = 28 x == 14 28 2 2x + 7y = 28

3. Warm-Up Exercises 2(0) + 7y = 28 Find the intercepts of the graph of an equation EXAMPLE 1 To find the y- intercept, substitute 0 for x and solve for y. Write original equation. Substitute 0 for x. Solve for y. ANSWER The x- intercept is 14. The y- intercept is 4. 2x +7y = 28 y = 28 7 = 4

4. Warm-Up Exercises Find the x- intercept and the y- intercept of the graph of the equation. GUIDED PRACTICE for Example 1 1. 3x + 2y = 6 ANSWER 2, 3

5. Warm-Up Exercises SOLUTION STEP 1 Use intercepts to graph an equation EXAMPLE 2 Graph the equation x + 2y = 4. x + 2y = 4 x =  x- intercept 4 Find the intercepts. x + 2(0) =4 0 + 2y = 4 y =  y- intercept 2 x + 2y = 4

6. Warm-Up Exercises Use intercepts to graph an equation EXAMPLE 2 STEP 2 Plot points. The x- intercept is 4, so plot the point (4, 0). The y- intercept is 2, so plot the point (0, 2). Draw a line through the points.

7. Warm-Up Exercises Use a graph to find intercepts EXAMPLE 3 The graph crosses the x- axis at (2, 0). The x- intercept is 2. The graph crosses the y- axis at (0, –1). The y- intercept is –1.

8. Warm-Up Exercises Use intercepts to graph an equation EXAMPLE 2 GUIDED PRACTICE for Examples 2 and 3 Graph the equation 6x + 7y = 42. Label the points where the line crosses the axes. 4. ANSWER

9. Warm-Up Exercises GUIDED PRACTICE for Examples 2 and 3 Identify the x- intercept and the y- intercept of the graph shown at the right. 5. –4, 2 ANSWER

10. Warm-Up Exercises Daily Homework Quiz 1. Find the x- intercept and the y- intercept of the graph of 3x – y = 3. x- int : 1, y- int : –3 ANSWER

11. Warm-Up Exercises Daily Homework Quiz 2.A recycling company pays $1 per used ink jet cartridge and $2 per used laser cartridge. The company paid a customer $14. This situation is given by x + 2y = 14 where x is the number of ink jet cartridges and y the number of laser cartridges. Use intercepts to graph the equation. Give four possibilities for the number of each type of cartridge that could have been recycled. ANSWER (0, 7), (6, 4), (10, 2), (14, 0)

12. You will graph a linear equation using intercepts. Essential question: How do you use intercepts to graph equations? Find the x- and y-intercepts by substituting 0 for y in the equation and solving for x and then 0 for x and solving for y. Plot the points that correspond to the intercepts and then connect the points by drawing a line or part of a line through them. The x-intercept is the x-coordinate of the point where the graph crosses the x- axis. The y-intercept is the y-coordinate of the point where the graph crosses the y- axis.