Question

Without​ graphing, tell whether the slope of a line that models the linear relationship is​ positive, negative,​ zero, or undefined. Then find the slope.Upper A babysitter earns $ 10 for 1 h and $ 30 for 3 h. find the slope

Answer 1

To determine the slope of the line that models the linear relationship between hours worked and earnings, we can use the formula for slope, which is:

\[
\text{slope} (m) = \frac{\text{change in earnings}}{\text{change in hours}}
\]

From the given information, we have two data points:
- For 1 hour: $10
- For 3 hours: $30

Now, let's calculate the changes:

1. Change in earnings: \(30 - 10 = 20\)
2. Change in hours: \(3 - 1 = 2\)

Now, substituting these values into the slope formula:

\[
m = \frac{20}{2} = 10
\]

The slope is \(10\), which is positive. This indicates that as the number of hours worked increases, the earnings also increase, confirming a positive relationship.

So, the slope is \(10\) and it is positive.