Math 1 · Unit 6 · Lesson 1 · part 3 of 5
Solve by graphing
Line 1: b = 1, m = 1.
Solve by graphing
- 1Graph both linesEach from m and b (Unit 3): plot b, step by m, draw. Rewrite into y = mx + b first if you need to.
- 2Read the crossing pointThe intersection, where the two lines share a point. Read its x and its y.
- 3Check it in both equationsPut the x and y into each equation. Both must come out true.
Worked: y = x + 1 and y = −2x + 7
Line 1: b = 1, m = 1. Line 2: b = 7, m = −2. They cross at (2, 3).
Check: 2 + 1 = 3, true. −4 + 7 = 3, true. Solution (2, 3).
Worked, with a rewrite: 2x + y = 4 and y = 12x − 1
Rewrite the first: y = −2x + 4. Graph both: they cross at (2, 0).
Check in the originals: 2(2) + 0 = 4, true. 12(2) − 1 = 0, true. Solution (2, 0).
The honest limit of graphingGraphing lets you see the answer, and it is the best way to understand what a solution is. But if the lines cross at a point like (73, 53), you cannot read that off a grid. That is why Lessons 2 and 3 teach two algebra methods that give the exact answer every time. Graph to see; use algebra to be exact.