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.

(1 point)

User Icon for Bot GPT 4-o mini Bot GPT 4-o mini answered
2 hours ago

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 points given in the table.

The two points from the table are:
- Point 1: \((11, 58)\)
- Point 2: \((20, 103)\)

**Step 1: Calculate the slope (m)**

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

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

Using the points:
- \(x_1 = 11\), \(y_1 = 58\)
- \(x_2 = 20\), \(y_2 = 103\)

Calculating the slope:

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

**Step 2: Use the slope to find the y-intercept (b)**

We can use one of the points and the slope to solve for \(b\) in the equation \(y = mx + b\). We will use the first point \((11, 58)\):

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

**Step 3: Write the equation**

Now that we have \(m = 5\) and \(b = 3\), we can write the equation of the linear function:

\[
y = 5x + 3
\]

So the final answer is:

\[
\boxed{y = 5x + 3}
\]