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Chapter 1: Problem 108

You have ascertained that a table of values of \(x\) and \(y\) corresponds to a linear function. How do you find an equation for that linear function?

Short Answer

Expert verified
To find the equation of a linear function given a table of values, follow these steps: 1. Calculate the slope (m) using the formula m = \( \frac{y2 - y1}{x2 - x1} \) with two points from the table. 2. Identify the y-intercept (b) either from the table or by using the formula b = y1 - m * x1 with the calculated slope and any point from the table. 3. Write the linear equation in the form y = mx + b, substituting the values of m and b obtained in previous steps.

Step by step solution

01

Calculate the slope (m)

We can find the slope by comparing the change in y-values to the change in x-values between two points in the table. If (x1, y1) and (x2, y2) are two points from the table, then the slope (m) can be calculated as: m = \( \frac{y2 - y1}{x2 - x1} \) Make sure to choose two points from the table and apply the formula to calculate the slope.
02

Identify the y-intercept (b)

To find the y-intercept, look for the point in the table where the x-value is 0. The corresponding y-value is the y-intercept (b). If the table doesn't have an x-value of 0, we can use the slope formula with the calculated slope (m) and any point (x1, y1) from the table to solve for b: b = y1 - m * x1 Make sure to substitute the x1 and y1 values from the selected point in the table and the calculated slope into the formula to find the y-intercept.
03

Write the linear equation in the form y = mx + b

Now that we have both the slope (m) and the y-intercept (b), we can write the equation of the linear function using the form y = mx + b. Make sure to substitute the values of m and b obtained in previous steps: y = m * x + b This is the equation of the linear function that corresponds to the given table of values.

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