Math 1 · Unit 3 · Lesson 4 · part 3 of 6
The four starting points, worked
The line crosses the y-axis at (0, −2), so b = −2.
The four starting points, worked
From a graph
The line crosses the y-axis at (0, −2), so b = −2. From (0, −2) to (2, 1): rise 3, run 2, so m = 32.
y = 32x − 2
From a table
x: 0, 1, 2, 3 and y: 7, 4, 1, −2. Each step of 1 in x drops y by 3: m = −3. The x = 0 row says b = 7.
y = −3x + 7
If the table were x: 2, 3, 4 and y: 11, 14, 17, then m = 3, and walking back: x = 1 gives 8, x = 0 gives 5. So b = 5 and y = 3x + 5.
From two points
(1, 5) and (3, 11). m = 11 − 53 − 1 = 62 = 3. Now use (1, 5): 5 = 3 × 1 + b, so 5 = 3 + b. Add −3 to both sides: b = 2.
y = 3x + 2
Check with the other point: 3 × 3 + 2 = 11. Yes.
From a slope and a point
Slope −2 through (4, 1). m = −2 already. Put in (4, 1): 1 = −2 × 4 + b, so 1 = −8 + b. Add 8 to both sides: b = 9.
y = −2x + 9
Why putting a point in finds bA point on the line is a true sentence about the line: its x and y make y = mx + b true. Once m is known, that sentence has only one unknown left, b, and it is a one-step equation from Unit 1.