Question

Use the table to answer the 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=−10x+78
y equals negative 10 x plus 78

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

y=10x−2
y equals 10 x minus 2

y=x+34

Answer 1

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

We have two points from the table:

\((4, 38)\) and \((6, 58)\).

1. **Calculate the slope \( m \)**:
The formula for the slope between two points \((x_1, y_1)\) and \((x_2, y_2)\) is:
\[
m = \frac{y_2 - y_1}{x_2 - x_1}
\]
Plugging in the values:
\[
m = \frac{58 - 38}{6 - 4} = \frac{20}{2} = 10
\]

2. **Find the y-intercept \( b \)**:
We will use the slope-intercept form of the equation, which is:
\[
y = mx + b
\]
We can substitute one of the points and our slope into this equation to solve for \( b \). Using the point \((4, 38)\):
\[
38 = 10(4) + b
\]
\[
38 = 40 + b
\]
\[
b = 38 - 40 = -2
\]

3. **Write the equation**:
Now that we have \( m = 10 \) and \( b = -2 \), the equation of the line is:
\[
y = 10x - 2
\]

Thus, the correct response from the list provided is:
**y = 10x - 2**.