Slope Math Example 4

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Example 4

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

Solution

  1. 1
    Step 1: Use the slope formula: m=y2−y1x2−x1m = \frac{y_2 - y_1}{x_2 - x_1}.
  2. 2
    Step 2: Substitute the coordinates: m=13−56−2=84m = \frac{13 - 5}{6 - 2} = \frac{8}{4}.
  3. 3
    Step 3: Simplify: m=2m = 2. The line rises 2 units for every 1 unit to the right.

Answer

m=2m = 2
The slope formula gives the rate of change between any two points on a line. A slope of 2 means the line is moderately steep, rising from left to right.

About Slope

A measure of the steepness and direction of a line, calculated as the ratio of vertical change (rise) to horizontal change (run) between any two points on the line. Slope is written as m=y2−y1x2−x1m = \frac{y_2 - y_1}{x_2 - x_1} and indicates how much yy changes for each unit increase in xx.

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More Slope Examples

Example 1 easy

Find the slope of the line passing through points [formula] and [formula].

Example 2 easy

Find the slope of the line through [formula] and [formula].

Example 3 medium

A line passes through [formula] and [formula]. What is its slope?

Example 5 hard

A line has slope [formula] and passes through [formula]. Find the [formula]-value when [formula].

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