Math worksheet for practicing writing linear equations in slope-intercept and standard forms.

Let's solve each problem step by step.

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Part 1: Write the slope-intercept form of the equation of each line.

The slope-intercept form is:

$$
y = mx + b
$$

where $ m $ is the slope and $ b $ is the y-intercept.

We need to solve each equation for $ y $.

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#### 1) $ 3x - 2y = -16 $

Solve for $ y $:
$$
-2y = -3x - 16
$$
$$
y = \frac{3}{2}x + 8
$$

✔ Answer: $ y = \frac{3}{2}x + 8 $

---

#### 2) $ 13x - 11y = -12 $

Solve for $ y $:
$$
-11y = -13x - 12
$$
$$
y = \frac{13}{11}x + \frac{12}{11}
$$

✔ Answer: $ y = \frac{13}{11}x + \frac{12}{11} $

---

#### 3) $ 9x - 7y = -7 $

Solve for $ y $:
$$
-7y = -9x - 7
$$
$$
y = \frac{9}{7}x + 1
$$

✔ Answer: $ y = \frac{9}{7}x + 1 $

---

#### 4) $ x - 3y = 6 $

Solve for $ y $:
$$
-3y = -x + 6
$$
$$
y = \frac{1}{3}x - 2
$$

✔ Answer: $ y = \frac{1}{3}x - 2 $

---

#### 5) $ 6x + 5y = -15 $

Solve for $ y $:
$$
5y = -6x - 15
$$
$$
y = -\frac{6}{5}x - 3
$$

✔ Answer: $ y = -\frac{6}{5}x - 3 $

---

#### 6) $ 4x - y = 1 $

Solve for $ y $:
$$
-y = -4x + 1
$$
$$
y = 4x - 1
$$

✔ Answer: $ y = 4x - 1 $

---

#### 7) $ 11x - 4y = 32 $

Solve for $ y $:
$$
-4y = -11x + 32
$$
$$
y = \frac{11}{4}x - 8
$$

✔ Answer: $ y = \frac{11}{4}x - 8 $

---

#### 8) $ 11x - 8y = -48 $

Solve for $ y $:
$$
-8y = -11x - 48
$$
$$
y = \frac{11}{8}x + 6
$$

✔ Answer: $ y = \frac{11}{8}x + 6 $

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Part 2: Write the standard form of the equation of the line through the given point with the given slope.

Standard form:
$$
Ax + By + C = 0 \quad \text{(or } Ax + By = C \text{)}
$$
where $ A, B, C $ are integers, and $ A \geq 0 $.

We'll use point-slope form first:
$$
y - y_1 = m(x - x_1)
$$
Then convert to standard form.

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#### 9) Through (1, 2), slope = 7

Point-slope:
$$
y - 2 = 7(x - 1)
$$
$$
y - 2 = 7x - 7
$$
$$
y = 7x - 5
$$

Now convert to standard form:
$$
-7x + y = -5
$$
Multiply both sides by $-1$ to make $ A > 0 $:
$$
7x - y = 5
$$

✔ Answer: $ 7x - y = 5 $

---

#### 10) Through (3, -1), slope = -1

Point-slope:
$$
y + 1 = -1(x - 3)
$$
$$
y + 1 = -x + 3
$$
$$
y = -x + 2
$$

Standard form:
$$
x + y = 2
$$

✔ Answer: $ x + y = 2 $

---

#### 11) Through (-2, 5), slope = -4

Point-slope:
$$
y - 5 = -4(x + 2)
$$
$$
y - 5 = -4x - 8
$$
$$
y = -4x - 3
$$

Standard form:
$$
4x + y = -3
$$

✔ Answer: $ 4x + y = -3 $

---

#### 12) Through (3, 5), slope = $ \frac{5}{3} $

Point-slope:
$$
y - 5 = \frac{5}{3}(x - 3)
$$

Multiply both sides by 3 to eliminate fractions:
$$
3(y - 5) = 5(x - 3)
$$
$$
3y - 15 = 5x - 15
$$
$$
3y = 5x
$$
$$
-5x + 3y = 0
$$

Or rearrange:
$$
5x - 3y = 0
$$

✔ Answer: $ 5x - 3y = 0 $

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✔ Final Answers:

#### Slope-Intercept Form:
1) $ y = \frac{3}{2}x + 8 $
2) $ y = \frac{13}{11}x + \frac{12}{11} $
3) $ y = \frac{9}{7}x + 1 $
4) $ y = \frac{1}{3}x - 2 $
5) $ y = -\frac{6}{5}x - 3 $
6) $ y = 4x - 1 $
7) $ y = \frac{11}{4}x - 8 $
8) $ y = \frac{11}{8}x + 6 $

#### Standard Form:
9) $ 7x - y = 5 $
10) $ x + y = 2 $
11) $ 4x + y = -3 $
12) $ 5x - 3y = 0 $

Let me know if you'd like these boxed or formatted differently!