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Relationship Between Variables in the Equation of a Line Study Guide (page 2)

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Updated on Oct 3, 2011

Example

First, find the slope. Take the difference between the first two y values and divide it by the difference between the first two x values: The slope of the line is 3. Next, find the y-intercept using the equation y = mx + b, the slope of the line, and one row of values from the table. Using the first row, we find that:

      –7 = 3(–2) + b
      –7 = –6 + b
      –1 = b

The y-intercept of the line is –1, making the equation y = 3x – 1.

Tip:

To find the slope and y-intercept using an input/output table, choose the rows of the table that contain the easiest numbers with which to work. The integers that are closest to zero are often the easiest values to add, subtract, multiply, and divide.

Finding the Missing Value in a Table

You might have noticed we only need two rows from a table to find the equation of the table. Sometimes, we are asked to find a missing value from a table. We start by finding the equation of the table, and then we use that equation to find the missing value.

Example

Using the first two rows of the table, we can find that the slope is = –7. Using the first row of the table, we can find the y-intercept of the equation:

      3 = –7(1) + b
      3 = –7 + b
      10 = b

The equation for this table is y = –7x + 10. We are looking for the value of y when x = 5, so substitute 5 for x in the equation and solve for y:

      y = –7(5) + 10
      y = –35 + 10
      y = –25

When x = 5, y = –25, so the missing value in the table is –25.

Tip:

The missing value in a table might be an x value. After finding the equation for the table, substitute the y value that is in the same row as the missing x value into the equation and solve for x.

Find practice problems and solutions for these concepts at Relationship Between Variables in the Equation of a Line Practice Questions.

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