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) y=10x-2 y=10x+2 y=-10x+78 y-x+34

Answer 1

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

Next, we need to calculate the slope (m) using the formula:
\[
m = \frac{y_2 - y_1}{x_2 - x_1}
\]
Where:
- \( (x_1, y_1) = (4, 38) \)
- \( (x_2, y_2) = (6, 58) \)

Plugging in the values:
\[
m = \frac{58 - 38}{6 - 4} = \frac{20}{2} = 10
\]

Now, we have the slope \( m = 10 \). Next, we use the slope-intercept form of a linear equation, \( y = mx + b \), to find the y-intercept \( b \).

We can use one of the points to find \( b \). Let's use the point (4, 38):
\[
38 = 10(4) + b
\]
\[
38 = 40 + b
\]
\[
b = 38 - 40 = -2
\]

Now we can write the equation of the line:
\[
y = 10x - 2
\]

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