EXAMPLE 2 Graph an equation using slope-intercept form

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Presentation transcript:

EXAMPLE 2 Graph an equation using slope-intercept form Graph the equation 2x + y = 3. SOLUTION STEP 1 Rewrite the equation in slope-intercept form. y –2x + 3 = Identify the slope and the y-intercept. STEP 2 = –2 m and = 3 b

EXAMPLE 2 Graph an equation using slope-intercept form STEP 3 Plot the point that corresponds to the y-intercept, (0, 3). STEP 4 Use the slope to locate a second point on the line. Draw a line through the two points.

EXAMPLE 3 Change slopes of lines ESCALATORS To get from one floor to another at a library, you can take either the stairs or the escalator. You can climb stairs at a rate of 1.75 feet per second, and the escalator rises at a rate of 2 feet per second. You have to travel a vertical distance of 28 feet. The equations model the vertical distance d (in feet) you have left to travel after t seconds. Stairs: d = –1.75t + 28 Escalator: d = –2t + 28

EXAMPLE 3 Change slopes of lines a. Graph the equations in the same coordinate plane. b. How much time do you save by taking the escalator? SOLUTION a. Draw the graph of d = –1.75t + 28 using the fact that the d-intercept is 28 and the slope is –1.75. Similarly, draw the graph of d = –2t + 28. The graphs make sense only in the first quadrant.

EXAMPLE 3 Change slopes of lines The equation d = –1.75t + 28 has a t-intercept of 16. The equation d = –2t + 28 has a t-intercept of 14. So, you save 16 – 14 = 2 seconds by taking the escalator. b.

EXAMPLE 2 GUIDED PRACTICE Graph an equation using slope-intercept form for Examples 2 and 3 4. Graph the equation y = –2x + 5. ANSWER

EXAMPLE 2 GUIDED PRACTICE Graph an equation using slope-intercept form for Examples 2 and 3 WHAT IF? In Example 3, suppose a person can climb stairs at a rate of 1.4 feet second. How much time does taking the escalator save? 5. ANSWER 6 sec