Question

Find the slope of the line that is parallel and perpendicular to the following equation.

2x - y = 1

Answer 1

Note that.

Slopes of parallel line are equal

Slopes of perpendicular lines are negative reciprocals

So

• 2x-y=1
• y=2x-1

Compare to slope intercept form

• slope=m=2

Slope of the parallel line=2

Slope of the perpendicular line=-1/2

Answer 2

Slope of the line that is parallel: 2

Slope of the line that is perpendicular:
`-(1)/(2)`

Explanation:

For the parallel line:

Rewrite your equation to slope-intercept form: y = mx + b

y = mx + b

• m = slope
• b = y-intercept (when x = 0)

2x - y = 1 <== subtract 2x to both sides

-2x -2x

-y = -2x + 1 <== divide both sides by -1

/-1 /-1

y = 2x - 1

The slope of the line that is parallel to this line is 2.

For the perpendicular line:

*Perpendicular lines have negative reciprocals*

Steps:

1. Take your original slope (2)

2. Flip it (1/2)

3. Change the sign (-1/2)

For a slope of 2, the reciprocal would be:
`-(1)/(2)`

Hope this helps!