The given line passes through the points and (4, 1).

on a coordinate plane, a line goes through (negative 4, negative 3) and (4, 1).

what is the equation, in point-slope form, of the line that is perpendicular to the given line and passes through the point (, 3)?

Step-by-step explanation:

The complete question is

The given line passes through the points (−4, −3) and (4, 1).

What is the equation, in point-slope form, of the line that is perpendicular to the given line and passes through the point (−4, 3)?

step 1

Find the slope of the given line

The formula to calculate the slope between two points is equal to

we have

(−4, −3) and (4, 1)

substitute the values

step 2

Find the slope of the perpendicular line to the given line

we know that

If two lines are perpendicular, then their slopes are opposite reciprocal (the product of their slopes is equal to -1)

so

we have

---> slope of the given line

so

---> slope of the perpendicular line to the given line

step 2

Find the equation in point slope form

we have

substitute

----> equation in point slope form