Slope of a Line

Summary

This math recipe will help you find the slope of a line in the XY Plane, whose equation is known.

Skill Level

Easy

Time

Approx. 15 sec

Ingredients

Equation of the line: \(ax + by + c = 0\)

Method

To determine the slope (\(m\)) of the line, we’ll use the following formula

\(m = –\frac{b}{a}\)

Examples

Example 1 Find the slope of the line \(3y = 4x + 12\).

Solution First, we’ll rearrange the terms to make the equation of the form \(ax + by + c = 0\). We’ll get

\(–4x + 3y – 12 = 0\)

Now, we’ll use the formula for the slope:

\(m = –\frac{–4}{3} = \frac{4}{3}\)

Therefore, the slope of the line equals \(\frac{4}{3}\). The following figure shows the line on the \(XY\) plane.

Slope of a Line

Example 2 Find the slope of the line \(2x + y = 4\).

Solution We’ll first rearrange the terms of the equation to get:

\(2x + y – 4 = 0\)

Now, let’s use the formula for the slope:

\(m = –\frac{2}{1} = –2\)

Therefore, the slope of the line equals \(–2\). The following figure shows the line on the \(XY\) plane.

Slope of a Line

 

Example 3 Find the slope the line \(3y – 6 = 0\).

Solution The equation can be rewritten as:

\(0x + 3y – 6 = 0\)

Now, let’s use the formula for the slope:

\(m = –\frac{0}{3} = 0\)

Therefore, the slope of the line equals \(0\). The following figure shows the line on the XY\) plane.

Slope of a Line

Example 4 Find the slope of the line \(2x = 8\).

Solution Let’s rearrange the equation first. We’ll get:

\(2x – 8 = 0\) or \(2x + 0y – 8 = 0\)

Now, let’s use the formula given above:

\(m = –\frac{2}{0}\), which is undefined.

Therefore, the slope of the line is undefined. The following figure shows the line on the \(XY\) plane.

Slope of a Line

That’s it for this recipe. Hope you found it helpful.

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