# How to Find 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.

### Finding Slope – 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 $$=\frac{y_{2} \ – \ y_{1}}{x_{2} \ – \ x_{1} }=\frac{5 \ – \ (- \ 9)}{2 \ – \ 1}=\frac{5 \ + \ 9}{1}=\frac{14}{1}=14$$

### Finding Slope – 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 $$=\frac{y_{2} \ – \ y_{1}}{x_{2} \ – \ x_{1} }=\frac{9 \ – \ 1}{- \ 2 \ – \ 6}=\frac{8}{-8}=\frac{1}{-1}=\ – \ 1$$

### Finding Slope – 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 $$=\frac{y_{2}- y_{1}}{x_{2} – x_{1} }=\frac{6-(-10)}{3 – 2}=\frac{6+10}{1}=\frac{16}{1}=16$$

### Finding Slope – 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 for Finding Slope

### 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. $$\color{blue}{(6, – 12), (15, – 3)}$$

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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