Finding Slope

Finding Slope

The slope of a line shows the direction of the line. In this article, you learn how to find the slope of a line.

Step by step guide to solve finding slope

  • The slope of a line represents the direction of a line on the coordinate plane.
  • A coordinate plane contains two perpendicular number lines. The horizontal line is \(x\) and the vertical line is \(y\). The point at which the two axes intersect is called the origin. An ordered pair \((x, y)\) shows the location of a point.
  • A line on the coordinate plane can be drawn by connecting two points.
  • To find the slope of a line, we need two points.
  • The slope of a line with two points A \((x_{1},y_{1})\) and B \((x_2,y_2)\) can be found by using this formula: \(\color{blue}{\frac{y_{2} \ – \ y_{1}}{x_{2} \ – \ x_{1}} =\frac{rise}{run}}\)
  • We can also find the slope of a line when we have its equation. The equation of a like is usually written in the form of: \(y=mx+b\), where \(m\) is the slope of the line and \(b\) is the \(y\)-intercept.

Example 1:

Find the slope of the line through these two points: \((1,–9)\) and \((2,5) \).

Solution:

Slope \(=\frac{y_{2} \ – \ y_{1}}{x_{2} \ – \ x_{1} }\). Let \((x_{1},y_{1} )\) be \((1,- \ 9) \) and \((x_{2},y_{2} )\) be \((2,5)\). Then: slope \(=\frac{y_{2} \ – \ y_{1}}{x_{2} \ – \ x_{1} }=\frac{5 \ – \ (- \ 9)}{2 \ – \ 1}=\frac{5 \ + \ 9}{1}=\frac{14}{1}=14\)

Example 2:

Find the slope of a line with these two points: \((6,1)\) and \((-2,9)\).

Solution:

Slope \(=\frac{y_{2} \ – \ y_{1}}{x_{2} \ – \ x_{1} }\). Let \((x_{1},y_{1} )\) be \((6,1) \) and \((x_{2},y_{2} )\) be \((-2,9)\). Then: slope \(=\frac{y_{2} \ – \ y_{1}}{x_{2} \ – \ x_{1} }=\frac{9 \ – \ 1}{- \ 2 \ – \ 6}=\frac{8}{-8}=\frac{1}{-1}=\ – \ 1\)

Example 3:

Find the slope of a line with these two points: \((2,–10)\) and \((3,6)\).

Solution:

Slope \(=\frac{y_{2}- y_{1}}{x_{2 } – x_{1 }}\). Let \((x_{1},y_{1} )\) be \((2,-10) \) and \((x_{2},y_{2} )\) be \((3,6)\). Then: slope \(=\frac{y_{2}- y_{1}}{x_{2} – x_{1} }=\frac{6-(-10)}{3 – 2}=\frac{6+10}{1}=\frac{16}{1}=16\)

Example 4:

Find the slope of the line with equation \(y=3x+6\)

Solution:

when the equation of a line is written in the form of \(y=mx+b\), \(m\) is the slope of the line. Then, in this line with equation \(y=3x+6\), the slope is 3.

Exercises

Find the slope of the line through each pair of points.

  1. \(\color{blue}{(1, 1), (3, 5)}\)
  2. \(\color{blue}{(4, – 6), (– 3, – 8)}\)
  3. \(\color{blue}{(7, – 12), (5, 10)}\)
  4. \(\color{blue}{(19, 3), (20, 3)}\)
  5. \(\color{blue}{(15, 8), (– 17, 9)}\)
  6. \(\color{blue}{(6, – 12), (15, – 3)}\)

Download Finding Slope Worksheet

Answers

  1. \(\color{blue}{2}\)
  2. \(\color{blue}{\frac{2}{7}}\)
  3. \(\color{blue}{-11}\)
  4. \(\color{blue}{0}\)
  5. \(\color{blue}{-\frac{1}{32}}\)
  6. \(\color{blue}{1}\)

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