The equation of a line that is perpendicular to y - 3 = -1(x - 2) and passes through the point (4, -1) is y = x - 5
Solution:
Given that we have to find the equation of a line that is perpendicular to y - 3 = -1(x - 2) and passes through the point (4, -1)
The slope intercept form is given as:
y = mx + c ----- eqn 1
Where "m" is the slope of line and "c" is the y - intercept
Given that the line that passes through the point ( 4, -1 ) and is perpendicular to the line y - 3 = -1(x - 2)
Given line is perpendicular to y - 3 = -1(x - 2)
y - 3 = -1(x - 2)
y - 3 = -x + 2
y = -x + 2 + 3
y = -x + 5
On comparing the above equation with eqn 1, we get slope of line , m = -1
We know that product of slope of a line and slope of line perpendicular to it is -1
-1 x slope of line perpendicular to it = -1
slope of line perpendicular to it = 1
Given point is (4, -1)
Now we have to find the equation of line passing through (4, -1) with slope m = 1
Substitute m = 1 and (x, y) = (4, -1) in eqn 1
-1 = 1(4) + c
-1 = 4 + c
c = -5
Substitute c = -5 and m = 1 in eqn 1 to get required equation of line
y = 1x - 5
y = x - 5
Thus the equation of line is found