Question

Rearrange the slope formula y=mx+b
𝑦
=
𝑚
𝑥
+
𝑏
for the quantity of interest m
𝑚
. Make sure to show each step.

Answer 1

To rearrange the slope formula \( y = mx + b \) for \( m \), we will follow these steps:

1. **Start with the original equation:**
\[
y = mx + b
\]

2. **Subtract \( b \) from both sides to isolate the terms involving \( m \):**
\[
y - b = mx
\]

3. **Now, divide both sides by \( x \) to solve for \( m \):**
\[
\frac{y - b}{x} = m
\]

4. **Finally, we can rewrite this to put \( m \) on the left side:**
\[
m = \frac{y - b}{x}
\]

Now, we have rearranged the slope formula to express \( m \) in terms of \( y \), \( b \), and \( x \):
\[
m = \frac{y - b}{x}
\]