EXAMPLE 2 Graphing Using Slope-Intercept Form

The y-intercept is 3, so plot the point (0, 3).STEP 1

The slope is , so plot a second point by12

STEP 2moving up 1 unit and right 2 units.

Draw a line through the points.STEP 3

Graph the equation y = x + 3.12

EXAMPLE 3 Writing a Function Rule

You are at the base of a trail on Mount Rainier in Washington. The temperature is 50.9°F. The temperature changes at a rate of –0.005°F per foot ofelevation as you hike up. What is the temperature 1000 feet above the base?

Hiking

SOLUTIONWrite a verbal model.STEP 1

EXAMPLE 3

STEP 2 Write an algebraic model in slope-intercept form.The temperature changes at a rate of –0.005°F per foot, so m = 0.005. The initial temperature is 50.9°F, so b = 50.9. Let y be the temperature and x be the change in elevation.

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Writing a Function Rule

y = m x + b Write slope-intercept form.

y = – 0.005 x + 50.9 Substitute –0.005 for m and 50.9 for b.

EXAMPLE 3 Writing a Function Rule

STEP 3 Find the value of y when x = 1000.

y = –0.005x + 50.9 Write the equation.

= –0.005(1000) + 50.9 Substitute 1000 for x.

= 45.9 Simplify.

The temperature 1000 feet above the base is 45.9°F.

ANSWER

GUIDED PRACTICE for Examples 2 and 3

Use the slope and y-intercept to graph the equation.

4. y = 2x + 5

GUIDED PRACTICE for Examples 2 and 3

5. y = 7x

GUIDED PRACTICE for Examples 2 and 3

6. – x + y = 6

GUIDED PRACTICE for Examples 2 and 3

7. What If? In Example 3, suppose the temperature at the base of the trail is 55.20 F. What is the temperature 2500 feet above the base?

The temperature 2500 feet above the base is 42.7°F.

ANSWER