Question

This table shows the relationship between x and y values that will contribute to linear functions.
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+78
y equals negative 10 x plus 78

y=10x−2
y equals 10 x minus 2

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

y=x+34

Answer 1

To find the equation of the linear function that models the relationship given in the table, we can first determine the slope (m) using the two points: (4, 38) and (6, 58).

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

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

Let's assign:
- \( (x_1, y_1) = (4, 38) \)
- \( (x_2, y_2) = (6, 58) \)

Now calculate the slope:

\[
m = \frac{58 - 38}{6 - 4} = \frac{20}{2} = 10
\]

Now that we have the slope \(m = 10\), we can use the point-slope form of the linear equation, which is:

\[
y - y_1 = m(x - x_1)
\]

Using point \((4, 38)\):

\[
y - 38 = 10(x - 4)
\]

Distribute the slope:

\[
y - 38 = 10x - 40
\]

Add 38 to both sides:

\[
y = 10x - 2
\]

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

\[
\boxed{y = 10x - 2}
\]