Question

Find the slope of a line parallel to the line whose equation is x - y = 8. Fully simplify your answer.
Answered by GPT 3.5
To find the slope of a line parallel to another line, we need to find the slope of the given line first.

Let's rearrange the equation x - y = 8 to slope-intercept form (y = mx + b), where m is the slope:

y = x - 8

Comparing this equation to the slope-intercept form, we can tell that the slope of the line is 1.

Since a parallel line has the same slope, the slope of a line parallel to x - y = 8 is also 1.
Answer
Find the slope of a line perpendicular to the line whose equation is 4x - 6y = -60. Fully simplify your answer.
Answered by GPT 3.5
To find the slope of a line perpendicular to another line, we need to find the slope of the given line first.

Let's rearrange the equation 4x - 6y = -60 to slope-intercept form (y = mx + b), where m is the slope:

-6y = -4x - 60

Dividing both sides by -6, we get:

y = (4/6)x + 10

Simplifying the equation, we have:

y = (2/3)x + 10

Comparing this equation to the slope-intercept form, we can tell that the slope of the line is 2/3.

To find the slope of a line perpendicular to this line, we can take the negative reciprocal of the given slope.

The negative reciprocal of 2/3 is -3/2.

Therefore, the slope of a line perpendicular to 4x - 6y = -60 is -3/2.