Algebra 1 / Unit 5: Linear Functions
5.3 Point-Slope and Standard Form
Notes
- Point-slope form: $y - y_1 = m(x - x_1)$ uses a point $(x_1, y_1)$ and the slope.
- Standard form: $Ax + By = C$. It makes intercepts easy: set $x = 0$ to find the $y$-intercept and $y = 0$ to find the $x$-intercept.
- All three forms can describe the same line.
Practice
Which is the point-slope form of the line through $(4, -1)$ with slope $\displaystyle \frac{1}{2}$?
$\displaystyle y - (-1) = \frac{1}{2}(x - 4)$.
What is the $x$-intercept of $3x + 5y = 30$?
Set $y = 0$: $3x = 30$.
The line through $(1, 2)$ and $(3, 8)$ in slope-intercept form is:
Slope $\displaystyle \frac{6}{2} = 3$; $2 = 3(1) + b$ gives $b = -1$.
Ready for more? Take the Unit 5 test.