Question

Use the table to answer the question.

Linear Function Equation Based on Given x and y Values
x
y

4 38
6 58
Write the equation of the linear function that models the relationship shown in the table.

(1 point)
Responses

y=10x−2
y equals 10 x minus 2

y=10x+2
y equals 10 x plus 2

y=−10x+78
y equals negative 10 x plus 78

y=x+34

Answer 1

To find the equation of the linear function that models the relationship shown in the table, we need to determine the slope \( m \) and the y-intercept \( b \) of the line.

We have two points from the table:
1. \( (4, 38) \)
2. \( (6, 58) \)

The formula for the slope \( m \) between two points \( (x_1, y_1) \) and \( (x_2, y_2) \) is given by:
\[
m = \frac{y_2 - y_1}{x_2 - x_1}
\]

Substituting in our points:
\[
m = \frac{58 - 38}{6 - 4} = \frac{20}{2} = 10
\]

Now we have the slope \( m = 10 \).

Next, we can use one of the points and the slope to find the y-intercept \( b \) using the equation of a line \( y = mx + b \). Let's use the point \( (4, 38) \):
\[
38 = 10(4) + b
\]
\[
38 = 40 + b
\]
\[
b = 38 - 40 = -2
\]

So, the equation of the linear function is:
\[
y = 10x - 2
\]

Thus, the correct response is:
**y = 10x - 2**