Question

Grant wrote an equation of a line through the point (4,1) that is perpendicular to the one shown. What other point lies on his line?

Answer 1

I have to see the line shown. We need the slope of the line shown.

Grant's line will have a slope that is a negative reciprocal of the line shown.

for example if the line has a slope of -3, Grant's perpendicular line will be 1/3.

To find the other point, use the slope formula: m = (y2-y1)/(x2-x1)

Answer 2

Another approach is to use:

y = mx + b

You will have m, x and y.
solve for b.

Write an equation where you have a value for m and b.

You can then figure out another x and y that will work in that equation.