Use the table to answer the question.

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 linear equation in the form \(y = mx + b\) using the given data points \((11, 58)\) and \((20, 103)\), we can follow these steps:

1. Calculate the slope \(m\): \[ m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{103 - 58}{20 - 11} = \frac{45}{9} = 5 \]

2. Use the slope and one of the points to find the y-intercept \(b\). We can use the point \((11, 58)\): \[ y = mx + b \implies 58 = 5(11) + b \] \[ 58 = 55 + b \implies b = 58 - 55 = 3 \]

3. Now we can write the equation of the line: \[ y = 5x + 3 \]

Thus, the equation of the linear function that models the relationship shown in the table is:

\[ y = 5x + 3 \]