Use the table to answer the question.

Question

This table shows the relationship between x and y values that will contribute to linear functions.
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.

(1 point)

Answer 1

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

First, we calculate the slope \(m\) using the two points given in the table: \((6, 16)\) and \((15, 43)\).

The formula for the slope \(m\) is:

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

Plugging in the values:

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

Now that we have the slope, \(m = 3\), we can use one of the points to find \(b\). We'll use the point \((6, 16)\).

The equation \(y = mx + b\) becomes:

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

Calculating this gives:

\[ 16 = 18 + b \]

To solve for \(b\), we subtract 18 from both sides:

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

Now we have both \(m\) and \(b\). Thus, the equation of the linear function is:

\[ y = 3x - 2 \]