Worksheet for finding the slope from linear equations.

Let's solve each problem step by step to find the slope of the line from the given equations.

We need to recall that the slope-intercept form of a line is:

$$
y = mx + b
$$

where:
- $ m $ is the slope
- $ b $ is the y-intercept

So, for each equation, we will rearrange it into the form $ y = mx + b $ and identify the coefficient of $ x $, which is the slope.

---

1) $ 5x + 3y + 12 = 0 $

Solve for $ y $:

$$
3y = -5x - 12 \\
y = -\frac{5}{3}x - 4
$$

✔ Slope = $ -\frac{5}{3} $

---

2) $ 7x - 9 = y $

This is already in the form $ y = mx + b $:

$$
y = 7x - 9
$$

✔ Slope = $ 7 $

---

3) $ -10 = 8x - y $

Solve for $ y $:

$$
-y = -8x + 10 \\
y = 8x - 10
$$

✔ Slope = $ 8 $

---

4) $ 4y - 15 = -3x $

Solve for $ y $:

$$
4y = -3x + 15 \\
y = -\frac{3}{4}x + \frac{15}{4}
$$

✔ Slope = $ -\frac{3}{4} $

---

5) $ x = 3 + 7y $

Solve for $ y $:

$$
x - 3 = 7y \\
y = \frac{1}{7}x - \frac{3}{7}
$$

✔ Slope = $ \frac{1}{7} $

---

6) $ 6x + 2y = -1 $

Solve for $ y $:

$$
2y = -6x - 1 \\
y = -3x - \frac{1}{2}
$$

✔ Slope = $ -3 $

---

7) $ 10x + 2y = -9 $

Solve for $ y $:

$$
2y = -10x - 9 \\
y = -5x - \frac{9}{2}
$$

✔ Slope = $ -5 $

---

8) $ 5y - 8x + 16 = 0 $

Solve for $ y $:

$$
5y = 8x - 16 \\
y = \frac{8}{5}x - \frac{16}{5}
$$

✔ Slope = $ \frac{8}{5} $

---

9) Find the slope of the line whose equation is $ 5x = -6y + 9 $

Solve for $ y $:

$$
5x - 9 = -6y \\
y = -\frac{5}{6}x + \frac{9}{6} \\
y = -\frac{5}{6}x + \frac{3}{2}
$$

✔ Slope = $ -\frac{5}{6} $

---

✔ Final Answers:

1) $ -\frac{5}{3} $
2) $ 7 $
3) $ 8 $
4) $ -\frac{3}{4} $
5) $ \frac{1}{7} $
6) $ -3 $
7) $ -5 $
8) $ \frac{8}{5} $
9) $ -\frac{5}{6} $

Let me know if you'd like these written in boxed format or explained further!