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)