Question

Functions Unit Test
11 of 1511 of 15 Items














Question
Use the table to answer the 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)
y=
x−

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 \( b \) using the two points given in the table.

The two points are (6, 16) and (15, 43).

### Step 1: Calculate the slope \( m \)

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

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

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

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

### Step 2: Use the slope and one of the points to find \( b \)

We can use the slope-intercept form \( y = mx + b \) and substitute one of the points. We'll use the point (6, 16):

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

Calculating \( 3(6) \):

\[
16 = 18 + b
\]

Now, solve for \( b \):

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

### Step 3: Write the equation

Now that we have \( m = 3 \) and \( b = -2 \), we can write the equation of the linear function:

\[
y = 3x - 2
\]

So the answer is:

\[
y = 3x - 2
\]