Equations of Linear Functions Practice

Question

Complete this assessment to review what you’ve learned. It will not count toward your grade.
3 of 53 of 5 Items

Question
Use the table to answer the question.

Determining the linear equation based on given data points.
\(x\) \(y\)
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)
\(y=\)
\(x+\)

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 given data points \((11, 58)\) and \((20, 103)\).

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 \((x_1, y_1) = (11, 58)\) and \((x_2, y_2) = (20, 103)\):

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

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

Now that we have \(m = 5\), we can use one of the points to solve for \(b\). We can use the point \((11, 58)\):

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

Step 3: Write the equation

Now we have the slope \(m = 5\) and the y-intercept \(b = 3\). Therefore, the equation of the linear function is:

\[ y = 5x + 3 \]

You can fill in your answer in the format specified:

\(y = 5x + 3\)