Math 1 · Unit 3 · Lesson 6 · part 3 of 5
Worked: intercepts, and the rewrite
2x + 3y = 12.
Worked: intercepts, and the rewrite
Intercepts from standard form
2x + 3y = 12.
y-intercept: x = 0, so 3y = 12, y = 4. The point (0, 4).
x-intercept: y = 0, so 2x = 12, x = 6. The point (6, 0).
Two points is enough to draw the line.
Standard form to y = mx + b
2x + 3y = 12. Get y alone, Unit 1 style. Step 1: 2x + 3y = 12 is already all addition. Add −2x to both sides: 3y = −2x + 12. Multiply both sides by 13: y = −23x + 4.
m = −23, b = 4. Check: b = 4 matches the y-intercept we found.
Point-slope to y = mx + b
y − 5 = 2(x − 3). Distribute: y − 5 = 2x − 6. Add 5 to both sides: y = 2x − 1.
m = 2, b = −1. Check with the point: 2 × 3 − 1 = 5. Yes.
Why the rewrite always worksGetting y alone is solving an equation for y, which is Unit 1: add the opposite of the x term to both sides, then multiply both sides by the reciprocal of the number on y. Two moves, and the line is back in the form that shows its numbers.