Question

Use the table to answer the 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=x+34 y equals x plus 34 y=10x+2 y equals 10 x plus 2 y=10x−2 y equals 10 x minus 2 y=−10x+78

Answer 1

To find the equation of the linear function that models the relationship between \( x \) and \( y \) from the table, we can start by identifying the two points provided: \( (4, 38) \) and \( (6, 58) \).

First, we calculate the slope \( m \) of the line using the formula:

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

Using the points \( (4, 38) \) and \( (6, 58) \):

- \( y_1 = 38 \)
- \( y_2 = 58 \)
- \( x_1 = 4 \)
- \( x_2 = 6 \)

Substituting the values into the slope formula:

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

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

Next, we can use the point-slope form of the equation \( y - y_1 = m(x - x_1) \). Using one of our points, let's use \( (4, 38) \):

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

Now, we simplify the equation:

\[
y - 38 = 10x - 40
\]
\[
y = 10x - 40 + 38
\]
\[
y = 10x - 2
\]

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

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

Hence, the correct response is \( y = 10x - 2 \).