Lesson 4: Graphing Linear Equations in Slope-Intercept Form

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).

Property

We can write the equation of any non-vertical line in slope-intercept form by solving the equation for $y$ in terms of $x$.

Caution: Do not confuse solving for $y$ with finding the $y$-intercept. When we solve for $y$, we are writing the equation in another form, so both variables, $x$ and $y$, still appear in the equation.

Examples

• To convert $6x + 3y = 12$, subtract $6x$ from both sides to get $3y = -6x + 12$. Then divide all terms by $3$ to get the final form $y = -2x + 4$.
• For the equation $5x - 2y = 10$, subtract $5x$ to get $-2y = -5x + 10$. Divide everything by $-2$ to find the slope-intercept form, $y = \frac{5}{2}x - 5$.
• To solve $x + 4y = 8$ for $y$, subtract $x$ from both sides giving $4y = -x + 8$. Then divide by $4$ to get $y = -\frac{1}{4}x + 2$.