Graph and interpret applications of slope–intercept
Many real-world applications are modeled by linear equations. We will take a look at a few applications here so you can see how equations written in slope–intercept form relate to real-world situations.
Usually when a linear equation models a real-world situation, different letters are used for the variables, instead of
x and
y . The variable names remind us of what quantities are being measured.
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.
Solution
ⓐ
ⓑ
ⓒ 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
[link] .
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.
ⓐ 50 inches
ⓑ 66 inches
ⓒ The slope, 2, means that the height,
h , increases by 2 inches when the shoe size,
s , increases by 1. The
h -intercept means that when the shoe size is 0, the height is 50 inches.
The equation
is used to estimate the temperature in degrees Fahrenheit,
T , based on the number of cricket chirps,
n , in one minute.
ⓐ Estimate the temperature when there are no chirps.
ⓑ Estimate the temperature when the number of chirps in one minute is 100.
ⓒ Interpret the slope and
T -intercept of the equation.
ⓓ Graph the equation.
ⓐ 40 degrees
ⓑ 65 degrees
ⓒ The slope,
, means that the temperature Fahrenheit (
F ) increases 1 degree when the number of chirps,
n , increases by 4. The
T -intercept means that when the number of chirps is 0, the temperature is
.
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