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Example 4.49 from Elementary Algebra, 4.5 Use the Slope–Intercept Form of an Equation of a Line
Use the Slope–Intercept Form of an Equation of a Line: example 4.49
The equation is used to convert temperatures, , on the Celsius scale to temperatures, , on the Fahrenheit scale.
ⓐ Find the Fahrenheit temperature for a Celsius temperature of 0.
ⓑ Find the Fahrenheit temperature for a Celsius temperature of 20.
ⓒ Interpret the slope and F-intercept of the equation.
ⓓ Graph the equation.
Work it out on paper first. Then open the solution one step at a time, and stop as soon as you can finish on your own.
Solution
ⓐ
Find the Fahrenheit temperature for a Celsius temperature of 0.
Find when .
Simplify.ⓑ
Find the Fahrenheit temperature for a Celsius temperature of 20.
Find when .
Simplify.
Simplify.Table 4.41ⓒ Interpret the slope and F-intercept of the equation.
Even though this equation uses and , it is still in slope–intercept form.
The slope, , means that the temperature Fahrenheit (F) increases 9 degrees when the temperature Celsius (C) increases 5 degrees.
The F-intercept means that when the temperature is on the Celsius scale, it is on the Fahrenheit scale.
ⓓ Graph the equation.
We’ll need to use a larger scale than our usual. Start at the F-intercept then count out the rise of 9 and the run of 5 to get a second point. See Figure 4.26.
Figure 4.26
Your turn
The book's Try It right after this example: same idea, new numbers. Only the answer is given.
The equation is used to estimate a woman’s height in inches, h, based on her shoe size, s.
- ⓐ Estimate the height of a child who wears women’s shoe size 0.
- ⓑ Estimate the height of a woman with shoe size 8.
- ⓒ Interpret the slope and h-intercept of the equation.
- ⓓ Graph the equation.
How did it go?