Integrated Math 1 / Unit 4: Linear Functions and Arithmetic Sequences
4.2 Slope-Intercept Form
Notes
Slope-intercept form is $y = mx + b$, where $m$ is the slope and $b$ is the $y$-intercept $(0, b)$.
- To graph: plot $(0, b)$, then use the slope (rise over run) to find more points.
- Read the slope and intercept directly from the equation.
- In context, $b$ is the starting value and $m$ is the rate of change.
- Example: $y = -3x + 7$ has slope $-3$ and $y$-intercept 7.
Practice
What are the slope and $y$-intercept of $y = -3x + 7$?
In $y = mx + b$, $m = -3$ and $b = 7$.
A line has slope $\displaystyle \frac{1}{2}$ and passes through $(0, -4)$. What is its equation?
The point $(0, -4)$ gives $b = -4$.
Which point is on the line $y = 2x - 1$?
$2(3) - 1 = 5$. The other points do not satisfy the equation.
Ready for more? Take the Unit 4 test.