What is the slope of a line perpendicular to the line whose equation is 3x−y=6. Fully simplify your answer.

Answer 1

To find the slope of a line given its equation, transform to slope-intercept form: y = mx+b. In that form the slope is the numerical coefficient of x.

For 3x - y = 6, visualize transposing the -y term to the right side of the equal sign (adding y to both sides is another way to think about it) and transpose the constant 6 to the left side of the equal sign (subtracting 6 from both sides is another way to think about it).

This results in 3x - 6 = y. Using the symmetric property for equality you can rewrite as:

y = 3x - 6.

So the slope of the given line is 3 (or 3/1).

Perpendicular lines (that are not horizontal or vertical) have slopes that are negative reciprocals (the product of the slopes is -1).

The reciprocal of 3 is 1/3. The negative (or opposite) reciprocal is -(1/3) or -1/3.

Here is a graph that depicts the above. Use the slider on b to see that the lines remain perpendicular regardless of the value of b.

desmos.com/calculator/0eeajavq5q

Visit the above graph by selecting the URL, right-clicking and choose Go to....