Use the table to answer the question.

Question

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 minus 2

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

y=10x+2

Answer 1

To find the equation of the linear function that models the relationship shown in the table, we can use the two points provided: (4, 38) and (6, 58).

First, we calculate the slope \( m \):

\[ m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{58 - 38}{6 - 4} = \frac{20}{2} = 10 \]

Next, we can use the point-slope form of the linear equation \( y - y_1 = m(x - x_1) \). We can use one of the points for this. Let's use the point (4, 38):

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

Expanding this:

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

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

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

Thus, the correct response is:

y = 10x - 2.