EXAMPLE 1 Finding Intercepts Find the intercepts of the graph of y = 1 2 x – 5.5. STEP 1 To find the x -intercept, let y = 0 and solve for x. 1 2 = y x.

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Presentation transcript:

EXAMPLE 1 Finding Intercepts Find the intercepts of the graph of y = 1 2 x – 5.5. STEP 1 To find the x -intercept, let y = 0 and solve for x. 1 2 = y x – 5 x – 5 0 =0 = 1 2 x – 5 5 =5 = 1 2 x 10 = x

EXAMPLE 1 Finding Intercepts STEP 2 To find the y -intercept, let x = 0 and solve for y. 1 2 y = x – y = (0) – 5 y = 0 – 5 y = – 5 ANSWER The x- intercept is 10 and the y- intercept is – 5. The graph of the equation crosses the x -axis at (10, 0) and the y -axis at (0, – 5).

EXAMPLE 2 Using Intercepts to Graph a Line Graph the line with an x -intercept of – 3 and a y - intercept of 2. The x -intercept is – 3, so plot the point (– 3, 0). The y -intercept is 2, The y -intercept is 2, so plot the point (0, 2). Then draw a line through the two points.

EXAMPLE 3 Deena runs and walks with her dog on a trail that is 8 miles long. She can run 4 miles per hour and walk 2 miles per hour. Graph the equation 4x + 2y = 8, where x is the number of hours she runs and y is the number of hours she walks. What do the intercepts represent? Fitness Using and Interpreting Intercepts

EXAMPLE 3 SOLUTION STEP 1 Find the x -intercept. 4x + 2y = 8 4x + 2(0) = 8 4x = 8 x = 2 STEP 2 Find the y- intercept. 4x + 2y = 8 4(0) + 2y = 8 2y = 8 y = 4 Using and Interpreting Intercepts

EXAMPLE 3 STEP 3 The x -intercept is 2 and the y- intercept is 4. So the points (2, 0) and (0, 4) are on the graph. Plot these points and draw a line through them. ANSWER The x -intercept represents the number of hours it takes Deena to run the entire time. The y -intercept represents the number of hours it takes Deena to walk the entire time. Using and Interpreting Intercepts

GUIDED PRACTICE for Examples 1, 2 and 3 Find the intercepts of the graph of the equation. Then graph the line using the intercepts. 1. y = 2x –10 The x - intercept is 5 and the y- intercept is –10. ANSWER

GUIDED PRACTICE for Examples 1, 2 and x + y = – 1 y = – 3x – 1 ANSWER 1 3 – The x -intercept is and the y - intercept is –1.

GUIDED PRACTICE for Examples 1, 2 and x + 3y = 18 3y = 18 – 5x y = 18 – 5x 3 The x -intercept is and the y- intercept is ANSWER

GUIDED PRACTICE for Examples 1, 2 and 3 In Example 3, suppose Deena runs and walks with her dog on a trail that is 12 miles long. Graph the equation 4x +2y = 12, where x is the number of hours she runs and y is the number of hours she walks. How are the intercepts affected by the change in the trail length? 4.4. What if? ANSWER Both intercepts are increased.