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Slope and the equation of a line

What slope measures, how to find it from two points, and how to write a line as y = mx + b.

1 分で読めます2026年10月18日 更新執筆：Sumzo teamレビュー：Sumzo team

The slope (or gradient) of a line measures how steep it is: how much yy changes for each step of 1 in xx. Lines rising to the right have positive slope; falling lines have negative slope.

m=y2−y1x2−x1=riserunm = \frac{y_2 - y_1}{x_2 - x_1} = \frac{\text{rise}}{\text{run}}

Every non-vertical line can be written as y=mx+by = mx + b, where mm is the slope and bb is the y-intercept (where the line crosses the y-axis).

解き方付き例題

Line through (1, 3) and (3, 7)

Find the equation of the line through (1,3)(1, 3) and (3,7)(3, 7).

解き方を表示
  1. Find the slope.
    m=7−33−1=2m = \frac{7 - 3}{3 - 1} = 2
  2. Substitute one point into y=mx+by = mx + b.
    3=2(1)+b⇒b=13 = 2(1) + b \Rightarrow b = 1

答え： y=2x+1y = 2x + 1

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