Question

Rearrange the slope formula y = mx + b for the quantitative interest in show all steps

Answer 1

The slope-intercept form of a linear equation is given by:

\[ y = mx + b \]

where:
- \( y \) is the dependent variable,
- \( m \) is the slope,
- \( x \) is the independent variable, and
- \( b \) is the y-intercept.

To rearrange this equation for \( x \), we can follow these steps:

1. **Isolate the term containing \( x \)**:
Start by subtracting \( b \) from both sides of the equation:

\[
y - b = mx
\]

2. **Solve for \( x \)**:
Now, to isolate \( x \), divide both sides of the equation by \( m \):

\[
x = \frac{y - b}{m}
\]

Now we have rearranged the slope formula \( y = mx + b \) to express \( x \) in terms of \( y \), \( m \), and \( b \):

\[
x = \frac{y - b}{m}
\]