Example 4

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 of elevation as you hike up. What is the temperature 1000 feet above the base?

HIKING

Writing an Equation

SOLUTION

STEP 1 Write a verbal model to describe the situation.

–

Example 4 Writing an Equation

STEP 2 Write a matching algebraic model in slope-intercept form. Let y be the temperature and x be the increase in elevation.

y = bmx + Write slope-intercept form.

STEP 3 Substitute for m and b. The temperature changes at a rate of 0.005°F per foot, so . The initial temperature is50.9°F, so b

–m = 0.005–

= 50.9.

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

0.005–

Example 4 Writing an Equation

STEP 4 Find the value of y when x = 1000.

Write the equation.y = 0.005x– 50.9+

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

Simplify.= 45.9

ANSWER

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

Guided Practice

10. WHAT IF? In Example 4, suppose the temperature at the base of the trail is 55.2°F. What is the temperature 2500 feet above the base?

ANSWER 42.7°F

for Example 4

11. CHARITY EVENT You are participating in a walk for charity. One donor will give you $4 for each mile you walk. Another donor gives you $25, a fixed amount that does not depend on how far you walk. How much money will you raise if you walk 6 miles?

ANSWER $49