Slope-intercept form

Definition

Slope-intercept form is a way of writing the equation of a line as $y = mx + b$, where $m$ represents the slope and $b$ represents the y-intercept. It is used to easily identify these two key properties of a linear function.

5 Must Know Facts For Your Next Test

1. The slope $m$ in $y = mx + b$ measures the steepness of the line, calculated as rise over run ($\frac{\Delta y}{\Delta x}$).
2. The y-intercept $b$ is the point where the line crosses the y-axis.
3. Parallel lines have identical slopes but different y-intercepts.
4. Perpendicular lines have slopes that are negative reciprocals of each other ($m_1 \cdot m_2 = -1$).
5. To convert from standard form $Ax + By = C$ to slope-intercept form, solve for $y$.

Review Questions

• What does each parameter in the equation $y = mx + b$ represent?
• How do you find the slope and y-intercept from an equation given in standard form?
• Explain how to determine if two lines are parallel or perpendicular using their slopes.

Related terms

Standard Form: A way to write linear equations as $Ax + By = C$, where A, B, and C are integers.

Point-Slope Form: $y - y_1 = m(x - x_1)$, an equation of a line that passes through point $(x_1, y_1)$ with slope $m$.

Linear Function: A function that graphs to a straight line; can be written in forms like slope-intercept or standard form.