x-Intercept Meets y-Intercept
When a line is described by where it cuts the axes, the intercept form is the cleanest way to write it.
Equation
y = -(2/2)*x + 2
Graph
Table
| x | y |
|---|---|
| -5 | 7 |
| -4 | 6 |
| -3 | 5 |
| -2 | 4 |
| -1 | 3 |
| 0 | 2 |
| 1 | 1 |
| 2 | 0 |
| 3 | -1 |
| 4 | -2 |
| 5 | -3 |
What this lesson covers
What you do
You shape the function y = -(b/a)*x + b and watch the graph answer.
Challenges to clear
- Cut the x-axis at 4 and the y-axis at 3: the form x/4 + y/3 = 1.
- Halfway across: at x = 2 the line sits at y = 1.5 — both intercepts in one equation.
- Cut the x-axis at 6 — slide a there.
- Now the y-intercept: halfway across at x = 3 the line must sit at 2. That gives the form x/6 + y/4 = 1.
Check yourself
Why does x/a + y/b = 1 instantly tell you the axis cuts?
- Set y = 0 to get x = a (x-intercept). Set x = 0 to get y = b (y-intercept). The form is built around those substitutions. — correct
- Because a and b are the slope and intercept respectively.
- Because it is a coincidence of notation; you still have to expand and rearrange.
- Because dividing always gives the axis intersection points.
Think about it
- If you double a, the line crosses the x-axis twice as far out. What happens to the steepness?