Write the slope- intercept form of the equation of the line described: through (-5,-1), perpendicular to y = -x - 5

Question

through (-5,-1), perpendicular to y = -x - 5

A) -4x + 1

B) y = x + 4

C) y = 4x + 1

D) y = x - 4

Answer 1

The slope-intercept form of a linear equation is y = mx + b. The variable m represents the slope and the variable b represents the y-intercept.

You're given that the line passes through the point (-5, -1), so you can start by plugging this coordinate point into the slope-intercept equation. This looks like (-1) = m(-5) + b.

Next, you know that the line you are solving for is perpendicular to the equation given. In order to find the slope of the new line, you need to know that perpendicular lines have opposite reciprocal slopes.

"Opposite" means that the two slopes will have opposite signs, so the opposite of a positive slope will be negative and the opposite of a negative slope will be positive. To get the "reciprocal" of a slope, you need to divide 1 by the slope, or you can think of it as writing the slope as a fraction (if it's not already written as one) and flipping the fraction upside down (swapping the numerator and the denominator). For example, the reciprocal of 1/2 is 2/1 or 2.

So the opposite reciprocal of the slope given -1 is 1, so m is 1.

Next, you can plug this into the slope-intercept equation to get (-1) = (1)(-5) + b. This equation now only has one missing variable b, which means you can isolate b to solve for it and find the last missing part of the equation you are looking for.

Once you isolate b, you should find that b is equal to 4. Having found b and m, you can plug these into the slope-intercept form to get the equation for the line that is perpendicular to the equation given and passes through the point (-5, -1).

Your answer should be y = x + 4, which is answer choice B.

Alternatively, since this is a multiple choice question, you could also solve this question by using the answer choices to help you.

First, eliminate any answer choices that are not in slope-intercept form, which is y = mx + b. The only answer choice not written in this form is A, so you can eliminate it.

Next, you can plug in the point given (-5, -1) to the remaining answer choices to see if any of the choices do not pass through the point. By doing this, you should see that C and D are both incorrect.

This leaves you with answer choice B, which is the correct answer as proven by the first explanation above.

Answer 2

Perpendicular lines have opposite, reciprocal slopes, like 3 and -1/3.

Which equation, if you plug in your given point, is true with the indicated slope?