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Determine the most convenient method to graph each line.

y = −6 5 x 3 y = 15 x = 7 y = 2 5 x 1 .

Solution

  1. y = −6
    This equation has only one variable, y . Its graph is a horizontal line crossing the y -axis at −6 .
  2. 5 x 3 y = 15
    This equation is of the form A x + B y = C . The easiest way to graph it will be to find the intercepts and one more point.
  3. x = 7
    There is only one variable, x . The graph is a vertical line crossing the x -axis at 7.
  4. y = 2 5 x 1
    Since this equation is in y = m x + b form, it will be easiest to graph this line by using the slope and y -intercept.
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Determine the most convenient method to graph each line: 3 x + 2 y = 12 y = 4 y = 1 5 x 4 x = −7 .

intercepts  horizontal line  slope–intercept  vertical line

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Determine the most convenient method to graph each line: x = 6 y = 3 4 x + 1 y = −8 4 x 3 y = −1 .

vertical line  slope–intercept  horizontal line  intercepts

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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 F = 9 5 C + 32 is used to convert temperatures, C , on the Celsius scale to temperatures, F , 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


Find the Fahrenheit temperature for a Celsius temperature of 0. F = 9 5 C + 32 Find F when C = 0 . F = 9 5 ( 0 ) + 32 Simplify. F = 32


Find the Fahrenheit temperature for a Celsius temperature of 20. F = 9 5 C + 32 Find F when C = 20. F = 9 5 ( 20 ) + 32 Simplify. F = 36 + 32 Simplify. F = 68

Interpret the slope and F -intercept of the equation.

Even though this equation uses F and C , it is still in slope–intercept form.

This image shows three lines of equations. The first line reads y equals m x plus b. The second line reads F equals m C plus b and the third line reads F equals nine fifths times C plus 32.

The slope, 9 5 , 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 0 ° on the Celsius scale, it is 32 ° on the Fahrenheit scale.

Graph the equation.

We’ll need to use a larger scale than our usual. Start at the F -intercept ( 0 , 32 ) then count out the rise of 9 and the run of 5 to get a second point. See [link] .

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The equation h = 2 s + 50 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.

  1. 50 inches
  2. 66 inches
  3. 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.

  4. The figure shows a line graphed on the x y-coordinate plane. The x-axis of the plane represents the variable s and runs from negative 2 to 15. The y-axis of the plane represents the variable h and runs from negative 1 to 80. The line begins at the point (0, 50) and goes through the points (8, 66).

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The equation T = 1 4 n + 40 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.

  1. 40 degrees
  2. 65 degrees
  3. The slope, 1 4 , 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 40 ° .

  4. The figure shows a line graphed on the x y-coordinate plane. The x-axis of the plane represents the variable n and runs from 10 to 140 The y-axis of the plane represents the variable T and runs from negative 5 to 75. The line begins at the point (0, 40) and goes through the point (100, 65).

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Source:  OpenStax, Elementary algebra. OpenStax CNX. Jan 18, 2017 Download for free at http://cnx.org/content/col12116/1.2
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