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+2

y=−10x+78

y=10x−2

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 that connects the points (4, 38) and (6, 58).

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

2. **Use the point-slope form to find the y-intercept (\(b\))**:
The equation of a line is usually written as:
\[
y = mx + b
\]
We can use one of the points to find \(b\). Let's use the point (4, 38):
\[
38 = 10(4) + b
\]
\[
38 = 40 + b
\]
\[
b = 38 - 40 = -2
\]

3. **Write the equation**:
Now substitute \(m = 10\) and \(b = -2\) into the equation:
\[
y = 10x - 2
\]

So, the equation of the linear function that models the relationship shown in the table is:
\[
\boxed{y = 10x - 2}
\]