BUILDING & PLANNING · FIELD TOOL
Slope-intercept form is y = mx + b: m is the slope and b is where the line crosses the y axis. Through (1, 5) and (4, 11) the slope is 6 ÷ 3 = 2, and b = 5 − 2 × 1 = 3, so y = 2x + 3. From standard form, y = −A ÷ B × x + C ÷ B: 2x + 3y = 12 gives y = −2/3x + 4.
Results update as you type.
Check the working before you order.
| Point-slope form | y − 5 = 2(x − 1) |
| Standard form | 2x − y = −3 |
| Slope m | 2 |
| y-intercept b | (0, 3) |
| x-intercept | (−3/2, 0) |
| Angle to the x axis | 63.43 ° |
Your prices are remembered on this device only.
Results are estimates for planning and material ordering only. They are not a substitute for structural design or approval by a qualified engineer. Read the full disclaimer.
y = mx + b
m = (y₂ − y₁) ÷ (x₂ − x₁)
b = y₁ − m × x₁
From Ax + By = C: m = −A ÷ B, b = C ÷ B
x-intercept = −b ÷ mLine through (1, 5) and (4, 11):
| Slope m | Angle | Rise per 10 along |
|---|---|---|
| 0.1 | 5.71° | 1 |
| 0.25 | 14.04° | 2.5 |
| 0.5 | 26.57° | 5 |
| 1 | 45° | 10 |
| 2 | 63.43° | 20 |
m is the slope: how much y goes up for each 1 along x. b is the y-intercept: the value of y where the line crosses the y axis, at x = 0.
Slope m = (y₂ − y₁) ÷ (x₂ − x₁), then b = y₁ − m × x₁. Through (1, 5) and (4, 11): m = 2, b = 3, so y = 2x + 3.
Solve for y. 2x + 3y = 12 → 3y = −2x + 12 → y = −2/3x + 4.
Set y = 0 and solve: x = −b ÷ m. For y = 2x + 3 the line crosses the x axis at x = −1.5.
Its x never changes, so the slope would be a rise divided by zero. It is written x = a number, such as x = 3.