Find the slope from two points

T.3 Find the slope from two points by Delta publications
  • Slope tells us how steep a line is.
  • It shows how much the y-value changes for every change in the x-value.
  • Slope is also called the rate of change or gradient.

If two points on a line are (x₁, y₁) and (x₂, y₂), the slope (m) is:

​m = y2 − y1 / x2 − x1

Read as:
Slope = Change in y ÷ Change in x
or
Slope = rise ÷ run


  1. Label the points: (x₁, y₁) and (x₂, y₂)
  2. Subtract y-values: y2−y1​ → this is the rise.
  3. Subtract x-values: x2−x1→ this is the run.
  4. Divide: rise / run
  5. Simplify the fraction if possible.

Find the slope of the line passing through (2, 5) and (6, 13):

m = 13−5 / 6−2 = 8/4 = 2

Slope = 2 → For every 1 unit you move right, the line goes up by 2 units.


  • Positive slope: Line goes up from left to right.
  • Negative slope: Line goes down from left to right.
  • Zero slope: Horizontal line (no rise).
  • Undefined slope: Vertical line (no run).

  • Mixing up x and y values.
  • Forgetting to subtract in the same order for both numerator and denominator.
  • Dividing by zero (happens in vertical lines → slope is undefined).

  • Slope is used in roads, ramps, roofs, and graphs to show steepness or rate of change.

Find the slope of the line that passes through (9, 4) and (2, 2).

Plug (9, 4) and (2, 2) into the slope formula.

Slope = change in y / change in x

= 2-4 / 2-9

= -2/-7

= 2/7

The slope is 2/7 .

Find the slope of the line that passes through (4, 3) and (6, 4).

Plug (4, 3) and (6, 4) into the slope formula.

Slope =change in y / change in x

= 4-3 / 6-4

= 1/2

The slope is 1/2

Simplify your answer and write it as a proper fraction, improper fraction, or integer.

Plug (2, 5) and (8, 4) into the slope formula.

slope = change in y / change in x

= 4 – 5 / 8 – 2 Plug in (25) and (84)

= -1 / 6 Subtract

The slope is -1 / 6 .

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