Slope-intercept form

Definition

Slope-intercept form is a way to express the equation of a straight line using the formula $y = mx + b$. In this formula, $m$ represents the slope and $b$ represents the y-intercept.

5 Must Know Facts For Your Next Test

1. The slope ($m$) indicates the steepness and direction of the line.
2. The y-intercept ($b$) is the point where the line crosses the y-axis.
3. To find $m$, you can use two points $(x_1, y_1)$ and $(x_2, y_2)$ with the formula $m = \frac{y_2 - y_1}{x_2 - x_1}$.
4. A positive slope means the line ascends from left to right, while a negative slope means it descends.
5. $y = mx + b$ can be derived from any linear equation by solving for $y$.

Review Questions

• What does the slope (m) represent in the equation $y = mx + b$?
• How do you determine the y-intercept (b) from a graph?
• Given two points on a line, how can you calculate its slope?

Related terms

Linear Equation:

An equation that makes a straight line when graphed. It typically has variables with no exponents higher than one.

Point-Slope Form:

$y - y_1 = m(x - x_1)$, another way to express linear equations using a point and its slope.

Standard Form:

$Ax + By = C$, another format for linear equations where A, B, and C are integers.