Question

Use the table to answer the question.

x
y
11 58
20 103
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 in the form \( y = mx + b \), we need to determine the slope \( m \) and the y-intercept \( b \).

1. First, calculate the slope \( m \) using the two points provided in the table: \( (11, 58) \) and \( (20, 103) \).

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

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

Substituting the points \( (11, 58) \) and \( (20, 103) \):

\[
m = \frac{103 - 58}{20 - 11} = \frac{45}{9} = 5
\]

2. Now we have the slope \( m = 5 \). To find the y-intercept \( b \), we can use one of the points. Let's use the point \( (11, 58) \).

Using the equation \( y = mx + b \):

\[
58 = 5(11) + b
\]
\[
58 = 55 + b
\]
\[
b = 58 - 55 = 3
\]

3. Now, we can write the equation of the linear function:

\[
y = 5x + 3
\]

Thus, the equation of the linear function that models the relationship shown in the table is \( \boxed{y = 5x + 3} \).