Find the Slope of a Line given the Equation

To find the slope of a line given its equation, the key is to rearrange the equation into the slope-intercept form:
\(y = mx + b\)
where:
\(m\) is the slope of the line.
\(b\) is the y-intercept (the point where the line crosses the y-axis).

The following diagram shows how to find the slope of a line given the equation. Scroll down the page for more examples and solutions for finding the slope of a line from the equation.

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Here’s how to find the slope from different forms of a linear equation:

1. Equation is already in Slope-Intercept Form \(y = mx + b\):
   If your equation looks like \(y = 5x - 3\), then the slope is simply the coefficient of \(x\). In this case, the slope \(m\) is 5.

2. Equation is in Standard Form \(Ax + By = C\):
   If your equation is in the form \(Ax + By = C\), you need to rearrange it to solve for \(y\) to get it into the slope-intercept form.
   Steps:
   a. Subtract \(Ax\) from both sides:
   \(By = −Ax + C\)
   b. Divide both sides by \(B\) (assuming \(B \neq 0\)):
   \(y = \frac{-A}{B} + \frac{C}{B}\)
   Now the equation is in the form \(y = mx + b\), where the slope \(m\) is \(-\frac{A}{B}\).
   

Example:
Equation: \(3x + 4y = 12\)
\(A = 3, B = 4, C = 12\)
Slope \(m\): \(-\frac{3}{4}\)

Example:
Equation: \(2x - 5y = 10\)
\(A = 2, B = -5, C = 10\)
Slope \(m\): \(-\frac{2}{-5} = \frac{2}{5}\)

Special cases:
For a horizontal line with the equation (y = c) (where (c) is a constant), the slope is 0.
For a vertical line with the equation (x = c) (where (c) is a constant), the slope is undefined.

Find slope of line from equation

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Finding Slope Using an Equation or Graph

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Finding the Slope of a Line from an Equation
How to use an equation to determine the slope of a line?

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