Question

Write the linear equation that gives the rule for this table.

x y
–80 –88
21 13
33 25
88 80


Write your answer as an equation with y first, followed by an equals sign.

Answer 1

To find the linear equation that fits the given points, we can first determine the slope (\(m\)) and y-intercept (\(b\)) of the line.

We can use the formula for the slope:

\[
m = \frac{y_2 - y_1}{x_2 - x_1}
\]

Let's take two points from the table, for instance, (21, 13) and (33, 25).

Using these points:

\[
m = \frac{25 - 13}{33 - 21} = \frac{12}{12} = 1
\]

Now we have a slope \(m = 1\). Next, we can use one of the points to find the y-intercept (\(b\)). We'll use the point (21, 13).

The equation of a line can be expressed as:

\[
y = mx + b
\]

Substitute \(m = 1\) and the point (21, 13):

\[
13 = 1(21) + b
\]

This simplifies to:

\[
13 = 21 + b
\]
\[
b = 13 - 21
\]
\[
b = -8
\]

Now we can write the equation of the line:

\[
y = 1x - 8
\]

This can be simplified to:

\[
y = x - 8
\]

Thus, the equation that gives the rule for the table is:

\[
y = x - 8
\]