Slope-intercept form

Definition

Slope-intercept form is a way to express the equation of a straight line. It is written as $y = mx + b$, where $m$ represents the slope and $b$ represents the y-intercept.

5 Must Know Facts For Your Next Test

1. The slope $m$ in the equation $y = mx + b$ measures the steepness of the line.
2. The y-intercept $b$ is the point where the line crosses the y-axis.
3. A positive slope indicates that the line ascends from left to right, while a negative slope indicates it descends.
4. Slope-intercept form can be derived from two points on a line using formulas for slope and intercepts.
5. The slope can also be calculated as $\frac{\Delta y}{\Delta x}$, which is the change in y divided by the change in x.

Review Questions

• What does 'm' represent in the slope-intercept form equation?
• If a line has an equation of $y = 2x + 3$, what are its slope and y-intercept?
• How would you convert an equation like $2x - 3y = 6$ into slope-intercept form?

Related terms

Point-Slope Form: An alternative way to express linear equations using a point $(x_1, y_1)$ and a slope m, written as $y - y_1 = m(x - x_1)$.

Linear Function:

A function whose graph produces a straight line, typically expressed in forms like $y = mx + b$.

Y-Intercept: The point at which a graph crosses the y-axis, represented by 'b' in the equation $y = mx + b$.