Question

Select the equations that are parallel and perpendicular to y = x + 5 and that pass through the point (-2, -1).

A. parallel: y = -x - 1
perpendicular: y = x + 2

B. parallel: y = x - 1
perpendicular: y = -x + 1

C. parallel: y = x + 1
perpendicular: y = -x - 3

D. parallel: y = 2x - 2
perpendicular: y = -2x - 1

Answer 1

The coefficient of 'x' in y = mx + b form of an equation gives you the slope of the equation. So the slope of the equation y = x + 5 is 1.

Parallel lines have the same slope, so in each of the choices given we can expect 'x' to have an coefficient of 1, that is, an equation of the form y = x + something

Perpendicular lines have slopes whose product is -1. So if 1 is the slope of a line, then the slope of the line perpendicular to it must be -1 since 1 * -1 = -1. So in each of the choices given you would expect 'x' to have a coefficient of -1, that is, an equation of the form y = -x + something

Answer 2

@navk could the answer be D?

Answer 3

@navk please check my answer

Answer 4

It's not D. From the parallel and perpendicular part we know that it can only be B or C since a parallel equation to y = x + 5 will be like 'y = x + something' while a perpendicular to it will be like y = -x + something

Answer 5

It is also given that the equations pass through the point (-2, -1) so try plugging in x = -2 and y = -1 into the options in B and C to get the correct choice

Answer 6

how do i do that? i can't really do this type of math