Question

Yesterday, Esperanza worked for 6 hours and earned $120. Today, Esperanza worked 8 hours and earned $156. Write the equation of the linear function that models the relationship between the number of hours Esperanza works and the amount of money she earns. Enter your answer in y=mx+b form.(1 point).

Answer 1

To find the equation of the linear function that models the relationship between the number of hours Esperanza works (x) and the amount of money she earns (y), we can use the points given:

From yesterday:
- Hours worked (x1) = 6
- Earnings (y1) = 120

From today:
- Hours worked (x2) = 8
- Earnings (y2) = 156

We start by calculating the slope (m) of the line using the formula:

\[
m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{156 - 120}{8 - 6} = \frac{36}{2} = 18
\]

Now we have the slope (m = 18). Next, we can use one of the points to find the y-intercept (b). We'll use the point (6, 120):

The equation of the line in point-slope form is:

\[
y - y_1 = m(x - x_1)
\]

Substituting in the values we have:

\[
y - 120 = 18(x - 6)
\]

Now, expand and simplify to get it into the form \(y = mx + b\):

\[
y - 120 = 18x - 108
\]
\[
y = 18x + 120 - 108
\]
\[
y = 18x + 12
\]

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

\[
y = 18x + 12
\]