Writing equations in slope intercept form worksheet: Fill out ... - Free Printable

Let's solve each problem step by step, starting with the slope-intercept form of a line:

$$
y = mx + b
$$

Where:
- $ m $ is the slope,
- $ b $ is the y-intercept.

We'll use this formula for problems where we're given a point and a slope (problems 1–9), or two points (problems 10–18). For problem 19, we’ll apply linear modeling to real-world data.

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Problems 1–3: Graphs with slope and point

We are given a graph showing a point and the slope. We'll use the point-slope form and then convert to slope-intercept form.

#### 1. Point: (-1, 4), Slope: $ m = -3 $

Use point-slope form:
$$
y - y_1 = m(x - x_1)
$$
$$
y - 4 = -3(x + 1)
$$
$$
y - 4 = -3x - 3
$$
$$
y = -3x + 1
$$

✔ Answer: $ y = -3x + 1 $

---

#### 2. Point: (4, 1), Slope: $ m = 1 $

$$
y - 1 = 1(x - 4)
$$
$$
y - 1 = x - 4
$$
$$
y = x - 3
$$

✔ Answer: $ y = x - 3 $

---

#### 3. Point: (-1, 2), Slope: $ m = 2 $

$$
y - 2 = 2(x + 1)
$$
$$
y - 2 = 2x + 2
$$
$$
y = 2x + 4
$$

✔ Answer: $ y = 2x + 4 $

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Problems 4–9: Given point and slope

Use $ y = mx + b $, plug in $ x $, $ y $, and $ m $, solve for $ b $.

#### 4. (1, 9); slope 4

$$
9 = 4(1) + b \Rightarrow 9 = 4 + b \Rightarrow b = 5
$$
$$
y = 4x + 5
$$

✔ Answer: $ y = 4x + 5 $

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#### 5. (4, 2); slope -2

$$
2 = -2(4) + b \Rightarrow 2 = -8 + b \Rightarrow b = 10
$$
$$
y = -2x + 10
$$

✔ Answer: $ y = -2x + 10 $

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#### 6. (2, -2); slope 3

$$
-2 = 3(2) + b \Rightarrow -2 = 6 + b \Rightarrow b = -8
$$
$$
y = 3x - 8
$$

✔ Answer: $ y = 3x - 8 $

---

#### 7. (3, 0); slope 5

$$
0 = 5(3) + b \Rightarrow 0 = 15 + b \Rightarrow b = -15
$$
$$
y = 5x - 15
$$

✔ Answer: $ y = 5x - 15 $

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#### 8. (-3, -2); slope 2

$$
-2 = 2(-3) + b \Rightarrow -2 = -6 + b \Rightarrow b = 4
$$
$$
y = 2x + 4
$$

✔ Answer: $ y = 2x + 4 $

---

#### 9. (-5, 4); slope -4

$$
4 = -4(-5) + b \Rightarrow 4 = 20 + b \Rightarrow b = -16
$$
$$
y = -4x - 16
$$

✔ Answer: $ y = -4x - 16 $

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Problems 10–12: Graphs with two points

We need to find slope first, then use one point to find $ b $.

#### 10. Points: (-2, 3), (3, -2)

Slope:
$$
m = \frac{-2 - 3}{3 - (-2)} = \frac{-5}{5} = -1
$$

Use point (-2, 3):
$$
3 = -1(-2) + b \Rightarrow 3 = 2 + b \Rightarrow b = 1
$$
$$
y = -x + 1
$$

✔ Answer: $ y = -x + 1 $

---

#### 11. Points: (-1, -3), (1, 1)

Slope:
$$
m = \frac{1 - (-3)}{1 - (-1)} = \frac{4}{2} = 2
$$

Use point (-1, -3):
$$
-3 = 2(-1) + b \Rightarrow -3 = -2 + b \Rightarrow b = -1
$$
$$
y = 2x - 1
$$

✔ Answer: $ y = 2x - 1 $

---

#### 12. Points: (0, 3), (2, -1)

Slope:
$$
m = \frac{-1 - 3}{2 - 0} = \frac{-4}{2} = -2
$$

Use (0, 3): This is already the y-intercept!
$$
b = 3
$$
$$
y = -2x + 3
$$

✔ Answer: $ y = -2x + 3 $

---

Problems 13–18: Two points (no graphs)

Same process: find slope → use point-slope → convert to slope-intercept.

#### 13. (1, 3), (-3, -5)

Slope:
$$
m = \frac{-5 - 3}{-3 - 1} = \frac{-8}{-4} = 2
$$

Use (1, 3):
$$
3 = 2(1) + b \Rightarrow b = 1
$$
$$
y = 2x + 1
$$

✔ Answer: $ y = 2x + 1 $

---

#### 14. (1, 4), (6, -1)

Slope:
$$
m = \frac{-1 - 4}{6 - 1} = \frac{-5}{5} = -1
$$

Use (1, 4):
$$
4 = -1(1) + b \Rightarrow b = 5
$$
$$
y = -x + 5
$$

✔ Answer: $ y = -x + 5 $

---

#### 15. (-1, -1), (3, 5)

Slope:
$$
m = \frac{5 - (-1)}{3 - (-1)} = \frac{6}{4} = \frac{3}{2}
$$

Use (-1, -1):
$$
-1 = \frac{3}{2}(-1) + b \Rightarrow -1 = -\frac{3}{2} + b \Rightarrow b = \frac{1}{2}
$$
$$
y = \frac{3}{2}x + \frac{1}{2}
$$

✔ Answer: $ y = \frac{3}{2}x + \frac{1}{2} $

---

#### 16. (-2, 4), (0, 6)

Slope:
$$
m = \frac{6 - 4}{0 - (-2)} = \frac{2}{2} = 1
$$

Use (0, 6): y-intercept is 6.
$$
y = x + 6
$$

✔ Answer: $ y = x + 6 $

---

#### 17. (3, 3), (1, -3)

Slope:
$$
m = \frac{-3 - 3}{1 - 3} = \frac{-6}{-2} = 3
$$

Use (3, 3):
$$
3 = 3(3) + b \Rightarrow 3 = 9 + b \Rightarrow b = -6
$$
$$
y = 3x - 6
$$

✔ Answer: $ y = 3x - 6 $

---

#### 18. (-1, 6), (3, -2)

Slope:
$$
m = \frac{-2 - 6}{3 - (-1)} = \frac{-8}{4} = -2
$$

Use (-1, 6):
$$
6 = -2(-1) + b \Rightarrow 6 = 2 + b \Rightarrow b = 4
$$
$$
y = -2x + 4
$$

✔ Answer: $ y = -2x + 4 $

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Problem 19: INVESTING

> 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 $ = price of stock
- $ w $ = number of weeks from now
- So, "two weeks ago" means $ w = -2 $
- "Seven weeks ago" means $ w = -7 $

We have two points:
- $ (-2, 74) $
- $ (-7, 59) $

#### a. Write a linear equation

Find slope:
$$
m = \frac{74 - 59}{-2 - (-7)} = \frac{15}{5} = 3
$$

So, the stock increases by $3 per week.

Now use point-slope with $ (-2, 74) $:
$$
p - 74 = 3(w + 2)
$$
$$
p = 3w + 6 + 74 = 3w + 80
$$

✔ Equation: $ p = 3w + 80 $

---

#### b. Estimate price five weeks ago

Five weeks ago → $ w = -5 $

$$
p = 3(-5) + 80 = -15 + 80 = 65
$$

✔ Answer: $65 per share

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✔ Final Answers Summary:

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 = \frac{3}{2}x + \frac{1}{2} $
16. $ y = x + 6 $
17. $ y = 3x - 6 $
18. $ y = -2x + 4 $
19a. $ p = 3w + 80 $
19b. $ \$65 $

Let me know if you'd like these checked against a key or explained further!