Question: What does it represent?
○ For each increase in the number of sheets filled, the number of signatures increases by 25.
○ For each increase in the number of signatures, the number of sheets filled increases by 25.
○ For each increase in the number of sheets filled, the number of signatures decreases by 25.
○ For each increase in the number of signatures, the number of sheets filled decreases by 25.
e. Graph your equation from part (a) on a coordinate plane.
Use the graphing tool to graph the equation.
top-left: small empty rectangle/box near the upper-left corner.$ [blank]
c. Lizzie surpassed her goal and received $360 from the hardware store.
How many doghouses did she build?
› Enter the answer in the space provided. Use numbers instead of words.
[blank] doghouses
d. What is the rate of change in this situation?
› Enter the answer in the space provided. Use numbers instead of words.
[blank]
graph shape: no visible graph; top-left shows a small dollar-sign label with an empty box, and lower-left shows two empty answer boxes; position_hint=top-left○ For each decrease in the number of doghouses made, the amount of money made increases by $45.
○ For each decrease in the amount of money made, the number of doghouses made increases by $45.
○ For each increase in the number of doghouses made, the amount of money made increases by $45.
○ For each increase in the amount of money made, the number of doghouses made increases by $45.
e. Graph your equation from part (a) on a coordinate plane.
Use the graphing tool to graph the equation.
Graph/text position_hint: centerAmount of Money Made (dollars)
Number of Doghouses
x
Graph shape: blank coordinate grid with x-axis labeled “Number of Doghouses” and y-axis labeled “Amount of Money Made (dollars)”; position_hint = center
1. **State the problem:**
Lizzie builds doghouses and earns money from the hardware store. We want to find how many doghouses she built if she received $360, and determine the rate of change.
2. **Define variables:**
Let $x$ = number of doghouses built.
Let $y$ = amount of money made.
3. **Identify the rate of change:**
From the problem, for each increase in the number of doghouses made, the amount of money made increases by 45.
This means the rate of change (slope) is $45$ dollars per doghouse.
4. **Write the linear equation:**
The general form is:
$$y = mx + b$$
where $m$ is the rate of change and $b$ is the initial amount of money when $x=0$.
Assuming Lizzie starts with $0$ money when no doghouses are built, $b=0$, so:
$$y = 45x$$
5. **Find the number of doghouses built when $y=360$:**
Substitute $y=360$:
$$360 = 45x$$
6. **Solve for $x$:**
Divide both sides by 45:
$$\frac{360}{\cancel{45}} = \frac{45x}{\cancel{45}}$$
$$8 = x$$
7. **Interpretation:**
Lizzie built $8$ doghouses to earn $360$.
8. **Rate of change:**
The rate of change is $45$ dollars per doghouse.
9. **Graphing:**
The graph is a straight line passing through the origin $(0,0)$ with slope $45$, meaning for every 1 unit increase in $x$ (doghouses), $y$ (money) increases by 45.
**Final answers:**
- Number of doghouses built: $8$
- Rate of change: $45$