Question: Slope homomalsm
1) y = 4x - 8
2) f(x) = 4x - 8
0 = 4x - 8
3) 4x = -8
4) 4x = -8
4 4
5) x = 2
3) 3x + 2y = 12
2) f(x) = 3x + 2y = 12
2) 3x + 2(0) = 12
3x + 0 = 12
0 = 3x + 12
3) -3x = 12
4) -3x = 12
-3 3
5) x = 4
2) y = -3x + 12
2) f(x) = -3x + 12
0 = -3x + 12
3) 3x + 12
4) 3x + 12
3 3
5) x = 4
A line graph is shown in the top-right, and the work is centered and bottom-left.User: correct our answer using step by step
1. **State the problem:** We are given three equations and asked to find the value of $x$ when $y=0$ (i.e., find the x-intercept) for each.
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2. **Equation 1: $y = 4x - 8$**
- To find the x-intercept, set $y=0$:
$$0 = 4x - 8$$
- Add $8$ to both sides:
$$8 = 4x$$
- Divide both sides by $4$:
$$\frac{8}{\cancel{4}} = \frac{4x}{\cancel{4}} \implies 2 = x$$
- **Answer:** $x=2$
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3. **Equation 2: $3x + 2y = 12$**
- To find the x-intercept, set $y=0$:
$$3x + 2(0) = 12 \implies 3x = 12$$
- Divide both sides by $3$:
$$\frac{3x}{\cancel{3}} = \frac{12}{\cancel{3}} \implies x = 4$$
- **Answer:** $x=4$
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4. **Equation 3: $y = -3x + 12$**
- To find the x-intercept, set $y=0$:
$$0 = -3x + 12$$
- Add $3x$ to both sides:
$$3x = 12$$
- Divide both sides by $3$:
$$\frac{3x}{\cancel{3}} = \frac{12}{\cancel{3}} \implies x = 4$$
- **Answer:** $x=4$
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**Summary:**
- For $y=4x-8$, $x=2$
- For $3x+2y=12$, $x=4$
- For $y=-3x+12$, $x=4$
All steps are corrected and consistent with solving for the x-intercept by setting $y=0$ and isolating $x$.