Select the correct answer. ОА
Which equation represents the line that is perpendicular to y = $5 + 23 and passes through (-40,2012
- 15
y = - = - 30
= 5 + 52
= - 56
ОВ.
Ос. y =
OD.

The question is written kinda bad, so i take the next two assumptions:

The original line is:

y = 5*x + 23

And we want to find a perpendicular line that passes through the point (-40, 2012)

Suppose that we have a linear equation:

y = a*x + b

A perpendicular line to this one, will have a slope equal to -(1/a)

Then a random perpendicular line to the one above, is:

y = -(1/a)*x + c

In this case, we start with the line:

y = 5*x + 23

Then the family of perpendicular lines to this one, will be like:

y = (-1/5)*x + c

Where c can be any real number.

Now, we also want this line to pass through (-40, 2012)

This means that when x = -40, the value of y must be 2012

We could replace these values in our equation above and solve it for c.

2012 = -(1/5)*(-40) + c

2012 = 40/5 + c

2012 = 8 + c

2012 - 8 = c = 2004

Then the equation is:

y = -(1/5)*x + 2004.