Worksheet for practicing writing linear equations in slope-intercept form, including graph-based and point-based problems.

Since the user has set all options (ExplainAnswer, TeachTopic, GeneratePractice) to false, I will proceed directly to solving the problems presented in the image and providing the final answers in the required format.

The image contains a worksheet titled "Writing Equations in Slope-Intercept Form". It asks to write equations for lines based on given points and slopes or pairs of points. I will solve each problem step-by-step.

Part 1: Write an equation of the line that passes through the given point with the given slope.

The slope-intercept form is $y = mx + b$, where $m$ is the slope and $b$ is the y-intercept.
We can use the point-slope form $y - y_1 = m(x - x_1)$ and rearrange it, or substitute the point $(x_1, y_1)$ and slope $m$ into $y = mx + b$ to solve for $b$.

Problem 1:
- Point: $(-1, 4)$
- Slope ($m$): $-3$
- Equation: $y = mx + b$
- Substitute: $4 = -3(-1) + b$
- Simplify: $4 = 3 + b$
- Solve for $b$: $b = 4 - 3 = 1$
- Final Equation: $y = -3x + 1$

Problem 2:
- Point: $(4, 1)$
- Slope ($m$): $1$
- Equation: $y = mx + b$
- Substitute: $1 = 1(4) + b$
- Simplify: $1 = 4 + b$
- Solve for $b$: $b = 1 - 4 = -3$
- Final Equation: $y = x - 3$

Problem 3:
- Point: $(-1, 2)$
- Slope ($m$): $2$
- Equation: $y = mx + b$
- Substitute: $2 = 2(-1) + b$
- Simplify: $2 = -2 + b$
- Solve for $b$: $b = 2 + 2 = 4$
- Final Equation: $y = 2x + 4$

Problem 4:
- Point: $(1, 9)$
- Slope ($m$): $4$
- Equation: $y = mx + b$
- Substitute: $9 = 4(1) + b$
- Simplify: $9 = 4 + b$
- Solve for $b$: $b = 5$
- Final Equation: $y = 4x + 5$

Problem 5:
- Point: $(4, 2)$
- Slope ($m$): $-2$
- Equation: $y = mx + b$
- Substitute: $2 = -2(4) + b$
- Simplify: $2 = -8 + b$
- Solve for $b$: $b = 10$
- Final Equation: $y = -2x + 10$

Problem 6:
- Point: $(2, -2)$
- Slope ($m$): $3$
- Equation: $y = mx + b$
- Substitute: $-2 = 3(2) + b$
- Simplify: $-2 = 6 + b$
- Solve for $b$: $b = -8$
- Final Equation: $y = 3x - 8$

Problem 7:
- Point: $(3, 0)$
- Slope ($m$): $5$
- Equation: $y = mx + b$
- Substitute: $0 = 5(3) + b$
- Simplify: $0 = 15 + b$
- Solve for $b$: $b = -15$
- Final Equation: $y = 5x - 15$

Problem 8:
- Point: $(-3, -2)$
- Slope ($m$): $2$
- Equation: $y = mx + b$
- Substitute: $-2 = 2(-3) + b$
- Simplify: $-2 = -6 + b$
- Solve for $b$: $b = 4$
- Final Equation: $y = 2x + 4$

Problem 9:
- Point: $(-5, 4)$
- Slope ($m$): $-4$
- Equation: $y = mx + b$
- Substitute: $4 = -4(-5) + b$
- Simplify: $4 = 20 + b$
- Solve for $b$: $b = -16$
- Final Equation: $y = -4x - 16$

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Part 2: Write an equation of the line that passes through each pair of points.

First, find the slope ($m$) using the formula $m = \frac{y_2 - y_1}{x_2 - x_1}$.
Then, use one of the points and the calculated slope to find the y-intercept ($b$) using $y = mx + b$.

Problem 10:
- Points: $(-2, 3)$ and $(3, -2)$
- Slope ($m$): $\frac{-2 - 3}{3 - (-2)} = \frac{-5}{5} = -1$
- Use point $(-2, 3)$: $3 = -1(-2) + b$
- Simplify: $3 = 2 + b$
- Solve for $b$: $b = 1$
- Final Equation: $y = -x + 1$

Problem 11:
- Points: $(-1, -3)$ and $(1, 1)$
- Slope ($m$): $\frac{1 - (-3)}{1 - (-1)} = \frac{4}{2} = 2$
- Use point $(1, 1)$: $1 = 2(1) + b$
- Simplify: $1 = 2 + b$
- Solve for $b$: $b = -1$
- Final Equation: $y = 2x - 1$

Problem 12:
- Points: $(0, 3)$ and $(2, -1)$
- Slope ($m$): $\frac{-1 - 3}{2 - 0} = \frac{-4}{2} = -2$
- Use point $(0, 3)$: Since the x-coordinate is 0, this is the y-intercept. So $b = 3$.
- Final Equation: $y = -2x + 3$

Problem 13:
- Points: $(1, 3)$ and $(-3, -5)$
- Slope ($m$): $\frac{-5 - 3}{-3 - 1} = \frac{-8}{-4} = 2$
- Use point $(1, 3)$: $3 = 2(1) + b$
- Simplify: $3 = 2 + b$
- Solve for $b$: $b = 1$
- Final Equation: $y = 2x + 1$

Problem 14:
- Points: $(1, 4)$ and $(6, -1)$
- Slope ($m$): $\frac{-1 - 4}{6 - 1} = \frac{-5}{5} = -1$
- Use point $(1, 4)$: $4 = -1(1) + b$
- Simplify: $4 = -1 + b$
- Solve for $b$: $b = 5$
- Final Equation: $y = -x + 5$

Problem 15:
- Points: $(1, -1)$ and $(3, 5)$
- Slope ($m$): $\frac{5 - (-1)}{3 - 1} = \frac{6}{2} = 3$
- Use point $(1, -1)$: $-1 = 3(1) + b$
- Simplify: $-1 = 3 + b$
- Solve for $b$: $b = -4$
- Final Equation: $y = 3x - 4$

Problem 16:
- Points: $(-2, 4)$ and $(0, 6)$
- Slope ($m$): $\frac{6 - 4}{0 - (-2)} = \frac{2}{2} = 1$
- Use point $(0, 6)$: This is the y-intercept, so $b = 6$.
- Final Equation: $y = x + 6$

Problem 17:
- Points: $(3, 3)$ and $(1, -3)$
- Slope ($m$): $\frac{-3 - 3}{1 - 3} = \frac{-6}{-2} = 3$
- Use point $(3, 3)$: $3 = 3(3) + b$
- Simplify: $3 = 9 + b$
- Solve for $b$: $b = -6$
- Final Equation: $y = 3x - 6$

Problem 18:
- Points: $(-1, 6)$ and $(3, -2)$
- Slope ($m$): $\frac{-2 - 6}{3 - (-1)} = \frac{-8}{4} = -2$
- Use point $(3, -2)$: $-2 = -2(3) + b$
- Simplify: $-2 = -6 + b$
- Solve for $b$: $b = 4$
- Final Equation: $y = -2x + 4$

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Part 3: Word Problem

Problem 19:
"The price of a share of stock in XYZ Corporation was \$74 two weeks ago. Seven weeks ago, the price was \$59 a share."

Let $p$ be the price of a share.
Let $w$ be the number of weeks from now.

We have two data points:
1. "Two weeks ago" means $w = -2$. Price $p = 74$. Point: $(-2, 74)$
2. "Seven weeks ago" means $w = -7$. Price $p = 59$. Point: $(-7, 59)$

a. Write a linear equation to find the price $p$ of a share of XYZ Corporation stock $w$ weeks from now.

First, find the slope ($m$):
$m = \frac{p_2 - p_1}{w_2 - w_1} = \frac{74 - 59}{-2 - (-7)} = \frac{15}{5} = 3$

The slope represents the rate of change of the stock price per week. It is increasing by \$3 per week.

Now, use the point-slope form or slope-intercept form to find the equation. Let's use $p = mw + b$.
Substitute $m = 3$ and one point, say $(-2, 74)$:
$74 = 3(-2) + b$
$74 = -6 + b$
$b = 80$

So the equation is:
$p = 3w + 80$

b. Estimate the price of a share of stock five weeks ago.

"Five weeks ago" means $w = -5$.
Substitute $w = -5$ into the equation found in part (a):
$p = 3(-5) + 80$
$p = -15 + 80$
$p = 65$

The estimated price five weeks ago was \$65.

Final Answer:
1. $y = -3x + 1$
2. $y = x - 3$
3. $y = 2x + 4$
4. $y = 4x + 5$
5. $y = -2x + 10$
6. $y = 3x - 8$
7. $y = 5x - 15$
8. $y = 2x + 4$
9. $y = -4x - 16$
10. $y = -x + 1$
11. $y = 2x - 1$
12. $y = -2x + 3$
13. $y = 2x + 1$
14. $y = -x + 5$
15. $y = 3x - 4$
16. $y = x + 6$
17. $y = 3x - 6$
18. $y = -2x + 4$
19. a. $p = 3w + 80$
b. \$65