Slope / Slope-Intercept Calculator

• Choose whether you know two points, one point and a slope, slope-intercept form, or standard form.
• Enter the values you know, then click Calculate.
• Read the slope, y-intercept, x-intercept, line direction, and equivalent equation forms.
• Use the graph to see the line, the intercepts, and the rise/run triangle.
• Use quick picks to practice positive, negative, zero, undefined, and fractional slopes.

• For two points, it uses m = (y₂ − y₁)/(x₂ − x₁).
• For point + slope, it uses y − y₁ = m(x − x₁), then solves for b.
• For slope-intercept form, it reads m and b directly.
• For standard form, it converts Ax + By = C into y = mx + b when possible.
• It then builds a graph, a value table, and a step-by-step explanation.

Example 1 — Find slope from two points

1. Suppose a line passes through (2, 3) and (6, 11).
2. Use m = (y₂ − y₁)/(x₂ − x₁).
3. Substitute: m = (11 − 3)/(6 − 2).
4. Simplify: m = 8/4 = 2.
5. The slope is 2, meaning the line rises 2 units for every 1 unit it moves right.

Example 2 — Convert to slope-intercept form

1. Suppose the line has slope m = -3 and passes through (2, 5).
2. Start with y = mx + b.
3. Substitute the point and slope: 5 = -3(2) + b.
4. Solve: 5 = -6 + b, so b = 11.
5. The slope-intercept form is y = -3x + 11.

Example 3 — Identify a vertical line

1. Suppose two points are (4, 2) and (4, 9).
2. The x-values are the same, so x₂ − x₁ = 0.
3. That makes the slope undefined because division by zero is not allowed.
4. The equation is x = 4, which is a vertical line.
5. A vertical line cannot be written in slope-intercept form because it is not a function of x.