Question

On a coordinate plane, a line goes through (negative 1, 1) and (0, negative 3). A point is at (negative 4, negative 3) and (0, negative 3). 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)? y + 3 = −4(x + 4) y + 3 = –One-fourth(x + 4) y + 3 = One-fourth(x + 4) y + 3 = 4(x + 4)

Answer 1

y + 3 = One-fourth(x + 4)

Explanation:

Just took the test and got it right

Answer 2

y + 3 = One-fourth(x + 4)

Step-by-step explanation:

Step 1:

First step is to find the slope of the line joining the 2 given points

(negative 1, 1) and (0, negative 3)

Formula for finding the slope of the line joining 2 given points is

Slope m = (change in y)/(change in x)

Using the above formula , the slope of the line joining the 2 given points

is m = (-3-1)/(0-(-1)) = -4/1 =-4

Step 2 :

Find the slope of the line perpendicular to the line joining the 2 given

points

Slopes of 2 perpendicular lines are negative reciprocals of each other

, i.e if m1 and m2 are slopes of 2 lines then m1*m2 = -1, if the lines are

perpendicular to each other.

Hence the slope of the line perpendicular to the line joining the above 2

given points is

m1*m2 = -1 => (-4)*m2 = -1 => m2 = 1/4

Step 3 :

Find the equation of the line with slope 1/4 and passes through the point (-4,-3)

Equation of a line passing through a given point and having a slope

of m is (y - y1) = m(x-x1).

Substituting slope as m= 1/4 and point (x1,y1) as (-4,-3) in the above equation,

(y-(-3)) = (1/4)(x-(-4))

=> y +3 = (1/4)(x+4)

=> y + 3 = One-fourth(x + 4)

Hence the required answer is y + 3 = One-fourth(x + 4)