Question

In slope-intercept form, y = mx + b,

Please classify which statements and terms belong with the m and which belong with the b.

Answer 1

In the slope-intercept form of a linear equation, \( y = mx + b \):

- **m** (the slope):
- Represents the rate of change of \( y \) as \( x \) changes.
- Indicates how steep the line is.
- If \( m > 0 \), the line slopes upward (positive slope).
- If \( m < 0 \), the line slopes downward (negative slope).
- It can be interpreted as the change in \( y \) for a one-unit increase in \( x \).

- **b** (the y-intercept):
- Represents the value of \( y \) when \( x = 0\).
- Indicates where the line crosses the y-axis.
- It can be thought of as the starting point of the line on the y-axis.

In summary:
- **Terms and statements related to \( m \)**: slope, rate of change, steepness, positive or negative slope.
- **Terms and statements related to \( b \)**: y-intercept, starting value, point where the line crosses the y-axis.