Question

Write the equation of the linear function that models the relationship shown in the table. Enter your answer in y=mx+b form

x= -3 y=-1
x= -2 y= 2
x= -1 y= 5
x=0 y=8
x=1 y=11

Answer 1

To find the equation of the linear function in the form \(y = mx + b\), we will first determine the slope \(m\) and the y-intercept \(b\).

1. **Find the slope \(m\)**:

The slope \(m\) is calculated using the formula:

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

We can use any two points from the table. Let's use the points \((-1, 5)\) and \((0, 8)\):

\[
m = \frac{8 - 5}{0 - (-1)} = \frac{3}{1} = 3
\]

2. **Find the y-intercept \(b\)**:

To find the y-intercept \(b\), we can substitute one of the points into the equation \(y = mx + b\). We'll use the point \((0, 8)\):

\[
y = mx + b
\]

Substituting \(x = 0\) and \(y = 8\):

\[
8 = 3(0) + b \implies b = 8
\]

3. **Write the equation**:

Now that we have both the slope \(m = 3\) and the y-intercept \(b = 8\), we can write the equation of the linear function:

\[
y = 3x + 8
\]

Therefore, the equation of the linear function that models the relationship shown in the table is:

\[
\boxed{y = 3x + 8}
\]