Integrated Math 1 / Unit 4: Linear Functions and Arithmetic Sequences
4.4 Writing Equations of Lines
Notes
To write a line from two points: find the slope, then use a point to find $b$ (or use point-slope form).
- Parallel lines have equal slopes.
- Example: through $(1, 5)$ and $(3, 1)$: $\displaystyle m = \frac{1 - 5}{3 - 1} = -2$. Then $5 = -2(1) + b$, so $b = 7$ and $y = -2x + 7$.
- If a point is $(0, b)$, you can read the intercept directly.
- Check by substituting both points.
Practice
Which line passes through $(0, 3)$ and $(2, 7)$?
Slope is $\displaystyle \frac{7 - 3}{2 - 0} = 2$, and the $y$-intercept is 3.
Which line passes through $(1, 5)$ and $(3, 1)$?
$m = -2$. Then $5 = -2(1) + b$, so $b = 7$.
Which line is parallel to $y = 3x - 2$ and passes through $(0, 5)$?
Parallel lines have the same slope, 3, and the new line has $y$-intercept 5.
Ready for more? Take the Unit 4 test.