Anchor Any Point
Use the point-slope form to write the equation of a line through any specific point.
Equation
y = 2*(x - 0) + 0
Graph
Table
| x | y |
|---|---|
| -3 | -6 |
| -2 | -4 |
| -1 | -2 |
| 0 | 0 |
| 1 | 2 |
| 2 | 4 |
| 3 | 6 |
What this lesson covers
What you do
You shape the function y = m*(x - x1) + y1 and watch the graph answer.
Challenges to clear
- Anchor at (2, 3) with slope 1: set x1 = 2, y1 = 3, m = 1.
- Walk back along it: the same line passes (−1, 0) — three steps left, three down.
- Anchor the line at the point (−1, 4): set x1 to −1 and y1 to 4.
- Now find the slope that also carries it through (1, 8) — two right, four up.
Check yourself
Why do we write (x - x1) in the point-slope formula, not (x + x1)?
- Because x1 is a coordinate, and we subtract the anchor's x-value from the variable x to find the horizontal distance. — correct
- Because the formula requires subtraction to balance the equation.
- Because adding x1 would make the slope negative.
- It is just a convention; (x + x1) works if you change the sign of x1.
Think about it
- If you change the slope m, does the line still pass through (x1, y1)? Try it.