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Consider the line

5x-3y=-4

What is the slope of a line perpendicular to this line?

What is the slope of a line parallel to this line?

The slope of line is m when the equation is in the form y = mx + b.

We have 5x on the left side, so subtract it from both sides. This gives -3y = -5x - 4.

We need the y term by itself, so divide by each term in the equation by -3.

This gives y = 5x/3 + 4/3.

From here, it is seen to have slope 5/3.

To go back and solve the first question, a perpendicular line has slope -1/m.

Since m is 5/3, the perpendicular line would have slope -3/5.

Algebra

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