Question

Use the table to answer the question.

x
y
6 16
15 43
Write the equation of the linear function that models the relationship shown in the table. Enter your answer in y=mx+b
form.

Answer 1

To find the equation of the linear function that models the relationship shown in the table, we'll first determine the slope (m) using the two points given: (6, 16) and (15, 43).

The formula for the slope (m) between two points \((x_1, y_1)\) and \((x_2, y_2)\) is given by:

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

Substituting the points (6, 16) and (15, 43):

- \(x_1 = 6, y_1 = 16\)
- \(x_2 = 15, y_2 = 43\)

Calculating the slope:

\[
m = \frac{43 - 16}{15 - 6} = \frac{27}{9} = 3
\]

Now that we have the slope \(m = 3\), we can use the point-slope form of the equation to find the y-intercept \(b\). We can use one of the points, let's use (6, 16):

The equation in slope-intercept form is:

\[
y = mx + b
\]

Substituting for \(m\) and the point (6, 16):

\[
16 = 3(6) + b
\]

Calculating:

\[
16 = 18 + b
\]

Solving for \(b\):

\[
b = 16 - 18 = -2
\]

Now we have both the slope and the y-intercept. The equation of the linear function is:

\[
y = 3x - 2
\]

So, the equation in \(y = mx + b\) form is:

\[
\boxed{y = 3x - 2}
\]