Answer:
y=5
Step-by-step explanation:
Recall that for a linear equation y = mx + b,
the gradient of the line is m and the gradient of a line perpendicular to this line is the negative reciprocal of m,
i.e:
gradient of line perpendicular to gradient m = -1/m
In our case, we are given y = x+1.
Compared to the general equation above, gradient m = 1
hence the gradient of a perpendicular line = -1/m = -1/1 = -1
therefore the perpendicular line will take the form:
y = (-1) x + b
y = -x + b, where b is the y-intercept.
We are also given that the perpendicular line passes through (4,1), we simply substitute x = 4, y = 1 into the equation
y = -x + b
1 = -4 + b (add 4 to both sides)
1 + 4 = b
b = 5
Hence the y-intercept is y=5
