Question
The graph has a line that passes through (5, 0) and (15, 1). The y-axis is labeled "Amount in Dollaes", and shows 0, 5, 10, 15, 20, etc. The x-axis is labeled " hours", and shows 0, 1, 2, 3, 4, etc.
The graph illustrates how much Amanda makes babysitting her little cousins. Using the graph, predict how much Amanda will make if she babysits them for 10 hours.
The graph illustrates how much Amanda makes babysitting her little cousins. Using the graph, predict how much Amanda will make if she babysits them for 10 hours.
Answers
GPT-4o mini
To find out how much Amanda will make if she babysits for 10 hours, we first need to determine the equation of the line that connects the points (5, 0) and (15, 1).
1. **Calculate the slope (m)** of the line using the formula:
\[
m = \frac{y_2 - y_1}{x_2 - x_1}
\]
Where \((x_1, y_1) = (5, 0)\) and \((x_2, y_2) = (15, 1)\):
\[
m = \frac{1 - 0}{15 - 5} = \frac{1}{10}
\]
2. **Formulate the equation of the line** using the point-slope form \(y - y_1 = m(x - x_1)\). We'll use point (5, 0):
\[
y - 0 = \frac{1}{10}(x - 5)
\]
Simplifying this, we get:
\[
y = \frac{1}{10}x - \frac{1}{2}
\]
3. **Substitute x = 10** to find how much Amanda makes for 10 hours:
\[
y = \frac{1}{10}(10) - \frac{1}{2}
\]
\[
y = 1 - 0.5 = 0.5
\]
So, according to the graph and the calculation, if Amanda babysits for 10 hours, she will make **$0.50**.
1. **Calculate the slope (m)** of the line using the formula:
\[
m = \frac{y_2 - y_1}{x_2 - x_1}
\]
Where \((x_1, y_1) = (5, 0)\) and \((x_2, y_2) = (15, 1)\):
\[
m = \frac{1 - 0}{15 - 5} = \frac{1}{10}
\]
2. **Formulate the equation of the line** using the point-slope form \(y - y_1 = m(x - x_1)\). We'll use point (5, 0):
\[
y - 0 = \frac{1}{10}(x - 5)
\]
Simplifying this, we get:
\[
y = \frac{1}{10}x - \frac{1}{2}
\]
3. **Substitute x = 10** to find how much Amanda makes for 10 hours:
\[
y = \frac{1}{10}(10) - \frac{1}{2}
\]
\[
y = 1 - 0.5 = 0.5
\]
So, according to the graph and the calculation, if Amanda babysits for 10 hours, she will make **$0.50**.