If you are trying to find the slope using the slope intercept form, you need to convert the given equation to the incline intercept form first. Then you can easily see the slope by the slope segment shape.

Example 1:

Find the slope of 4x + 2y = 12

4x + 2y = 12

Subtract 4x from each side of the equation.

4x – 4x + 2y = 12 – 4x

0 + 2y = 12 – 4x

2y = 12 – 4x

2y = 12 + -4x

2y = -4x + 12

Divide each side of the equation by 2 so that the equation can be written in the form of a slope segment.

2y / 2 = (-4x + 12) / 2

y = -4x / 2 + 12/2

y = -2x + 6

The slope segment shape is y = mx + b and m is the slope.

Comparison of y = mx + b with y = -2x + 6 we can see that the slope m = -2. is

The slope of the line is -2.

Example # 2:

Find the slope of -5x + 3y = 8

-5x + 3y = 8

Add 5x to each side of the equation.

-5x + 5x + 3y = 8 + 5x

0 + 3y = 8 + 5x

3y = 5x + 8

Divide each side of the equation by 3 so that the equation can be written in the form of a slope segment.

3y / 3 = (5x + 8) / 3

y = 5x / 3 + 8/3

y = (5/3) x + 8/3

The slope of the line is 5/3.

A little tricky example that shows how to find the slope using the slope segment shape

Example # 3:

Find the slope of Ax + By = C

Ax + By = C

Subtract Ax from each side of the equation.

Ax – Ax + By = C – Ax

0 + By = C – Ax

By = C – Ax

By = C + -Ax

By = -Ax + C

Divide each side of the equation by B so that the equation can be written in the form of a slope.

By / B = (-Ax + C) / B

y = -Ax / B + C / B

y = (-A / B) x + C / B

The slope of the line is -A / B.



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