The Core Formula: Slope and Y-Intercept
The core formula relating slope and y-intercept is a foundational Grade 7 math skill from Yoshiwara Intermediate Algebra. The slope-intercept form y = mx + b defines a line using slope m (rate of change) and y-intercept b (where the line crosses the y-axis).
Key Concepts
Property The slope intercept form for a linear equation is $y = mx + b$, where $m$ is the slope of the line and the point $(0, b)$ is the y intercept.
The slope formula between two points $(x 1, y 1)$ and $(x 2, y 2)$ is $m = \frac{y 2 y 1}{x 2 x 1}$.
This formula calculates the ratio of the change in the y coordinates (rise) to the change in the x coordinates (run).
Common Questions
What is the slope-intercept form of a linear equation?
The slope-intercept form is y = mx + b, where m is the slope and b is the y-intercept — the point where the line crosses the y-axis.
How do you find slope and y-intercept from an equation?
In y = mx + b, the coefficient of x is the slope m, and the constant term is the y-intercept b. For example, in y = 3x - 2, slope = 3 and y-intercept = -2.
How do you graph a line using slope and y-intercept?
Start by plotting the y-intercept on the y-axis, then use the slope as rise-over-run to plot a second point, and draw a line through both points.
What does a negative slope mean in y = mx + b?
A negative slope means the line goes downward from left to right. Each unit increase in x decreases y by the absolute value of m.