1Cademy - Finding the Slope of the Line Between $$(1, 2)$$ and $$(4, 5)$$

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Slope Formula

Example

Finding the Slope of the Line Between $(1, 2)$ and $(4, 5)$

To find the slope of the line passing through the points $(1, 2)$ and $(4, 5)$ , apply the slope formula.

Label the points. Let $(1, 2)$ be point #1 so that $x_1 = 1$ and $y_1 = 2$ , and let $(4, 5)$ be point #2 so that $x_2 = 4$ and $y_2 = 5$ .

Write the slope formula:

$m = \frac{y_2 - y_1}{x_2 - x_1}$

Substitute the coordinates. First replace the $y$ -values in the numerator, then the $x$ -values in the denominator:

$m = \frac{5 - 2}{4 - 1}$

Simplify the numerator and the denominator:

$m = \frac{3}{3}$

Simplify the fraction:

$m = 1$

The slope is $1$ . This result can be confirmed on a graph by counting the rise and run between the two points: using $m = \frac{\text{rise}}{\text{run}}$ , the line rises $3$ units and runs $3$ units to the right, giving $\frac{3}{3} = 1$ . It does not matter which point is designated as point #1 and which as point #2 — swapping the labels produces the same slope.

Updated 2026-04-21

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OpenStax Elementary Algebra

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