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Linear functionsAlgebraMiddle schoolabout 0:45

Find the slope and equation of the line through (1, -2) and (5, 6): animated lesson

A narrated, step-by-step linear functions video lesson with captions. Final answer: m = 2; y = 2x - 4.

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Video with a synthetic English voice and captions. Pick another language for subtitles in that language, or open the interactive version.

Video narrated by a synthetic voice (Piper TTS, en_US-ljspeech-high voice (LJ Speech dataset, public domain)); the steps come from our maths engine and the answer was checked independently. Download MP4 (0.3 MB) · Captions (WebVTT)

Steps on screen

1. The problem
Slope between two points
Find the slope and equation of the line through (1, -2) and (5, 6).
2. Steps, part 1
1. $(x_1, y_1) = (1, -2),\quad (x_2, y_2) = (5, 6)$
  Label the points
2. $y_2 - y_1 = 6 - (-2) = 8$
  Find the change in y (rise)
3. $x_2 - x_1 = 5 - 1 = 4$
  Find the change in x (run)
4. $m = \frac{8}{4} = 2$
  Divide rise by run
3. Steps, part 2
1. $b = y_1 - m x_1 = -2 - 2 \cdot 1 = -4$
  Find the y-intercept using the first point
2. $y = 2x - 4$
  Write the equation of the line
4. The answer
$m = 2,\quad y = 2x - 4$
m = 8/4 = 2
5. Check
- Second point: 2·(5) + -4 = 6 (expected 6)

Transcript

The problem. Here is the problem: Find the slope and equation of the line through (1, negative 2) and (5, 6). Find the slope (rate of change) of the line through two points.

Steps, part 1. Label the points. Find the change in y (rise). Find the change in x (run). Divide rise by run.

Steps, part 2. Find the y-intercept using the first point. Write the equation of the line.

The answer. So the answer is m equals 2; y equals 2x minus 4. The slope is 2: for every 1 unit increase in x, y changes by 2. The line rises from left to right.

Check. Second point: 2 times (5) plus negative 4 equals 6 (expected 6).

About linear functions

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