5.2: Find y given x and the Equation of a Line

Learning Outcomes

  1. Find the value of y given x and the equation of a line.
  2. Use a line to make predictions.

A line can be thought of as a function, which means that if a value of x is given, the equation of the line produces exactly one value of y; This is particularly useful in regression analysis where the line is used to make a prediction of one variable given the value of the other variable.

Example 5.2.1

Consider the line with equation:

    \[y=3x-4\nonumber \]

Find the value of y when x is 5.

Solution

Just replace the variable x with the number 5 in the equation and perform the arithmetic:

    \[y\:=\:3\left(5\right)-4=15-4\:=11\nonumber \]

Example 5.2.2

A survey was done to look at the relationship between a woman’s height, x and the woman’s weight, y. The equation of the regression line was found to be:

    \[y=-220+5.5x\nonumber \]

Use this equation to estimate the weight in pounds of a woman who is 5′ 2″ (62 inches) tall.

Solution

Just replace the variable x with the number 62 in the equation and perform the arithmetic:

    \[y\:=\:-220+5.5\left(62\right)\nonumber \]

We can put this into a calculator or computer to get:

    \[y\:=\:121\nonumber \]

Therefore, our best prediction for the weight of a woman who is 5′ 2” tall is that she is 121 lbs.

Exercise

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Support for Elementary Statistics Copyright © by Larry Green and Adapted by Ram Subedi is licensed under a Creative Commons Attribution 4.0 International License, except where otherwise noted.

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