80 POINTS What is the y-intercept of the line perpendicular to the line y = x + 1 that includes the point (4, 1)? 2 4

Step-by-step explanation:

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

a

b

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step-by-step explanation: