Slope Calculator

First point (x1, y1)
Second point (x2, y2)

This slope calculator for two points finds how steep the line through your points is. Type in the x and y values of both points, and it shows the slope, the three standard line forms, and both intercepts. It is useful for algebra homework, coordinate geometry, and checking answers before a test.

How slope is found

Slope measures how much y changes for each unit x changes. The tool uses this formula: m = (y2 – y1) / (x2 – x1). The top of the fraction is called the rise, and the bottom is called the run. A positive slope climbs from left to right, a negative slope falls, and a slope of zero means the line is flat. Once you know the slope, the tool builds the point-slope form, rearranges it into slope-intercept form, and then into standard form, reading off the y-intercept and x-intercept along the way.

Worked example: slope through (2, 5) and (9, 19)

  1. Subtract the x values: 9 – 2 = 7 (the run).
  2. Subtract the y values: 19 – 5 = 14 (the rise).
  3. Divide: 14 / 7 = 2, so the slope is 2.
  4. Point-slope form: y – 5 = 2(x – 2).
  5. Slope-intercept form: y = 2x + 1, so the y-intercept is 1.
  6. Standard form: 2x – y = -1.
  7. X-intercept: -0.5, because 0 = 2x + 1 gives x = -0.5.

How to use this calculator

  1. Type the coordinates of your first point into the x1 and y1 boxes.
  2. Type the coordinates of your second point into the x2 and y2 boxes.
  3. Click “Calculate slope” to see the slope, the line forms, the intercepts, and the steps.

Limits of this tool

  • Two points only. It does not accept a point plus a slope, or a line equation. Those come later.
  • A vertical line (both x values the same) has no defined slope, so the tool shows an error instead of an answer.
  • Coordinates must be plain numbers. Letters and blank boxes are rejected.
  • It works with the line through your two points. It does not draw a graph or solve systems of equations.

Frequently asked questions

What does this slope calculator for two points show me?

It shows the slope, the point-slope, slope-intercept, and standard forms of the line, plus the y-intercept and the x-intercept, with each step of the working.

Why is the slope undefined for a vertical line?

Slope divides the rise by the run. On a vertical line the run (x2 – x1) is zero, and division by zero has no answer. That is why the tool reports an error instead of a number when both x values match.

What is the difference between point-slope and slope-intercept form?

Point-slope form (y – y1 = m(x – x1)) shows the slope and one point directly. Slope-intercept form (y = mx + b) shows the slope and the y-intercept directly. Both describe the same line; the tool gives you both.

How do I find the x-intercept from the slope and y-intercept?

Set y to 0 in y = mx + b and solve for x: x = -b / m. For the worked example above, x = -1 / 2 = -0.5.

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