Write an equation in slope-intercept form for the line that passes through the given point and is perpendicular to the graph of the equation. (3,−2); y=x+4 3 , - 2 ; y = x + 4

Question

Write a slope intercept form equation

Answer 1

Slope-intercept form is:

y = m x + b

Here m is the slope (change in y over the change in x, or the rise over the run, vertical change divided by horizontal change of the function) and b is the intercept (point at which the function intersects the y-axis). For a slope to be perpendicular, it should the negative reciprocal of the other slope. The reciprocal is found by flipping the numerator and the denominator of the slope. The perpendicular slope is found by placing a negative sign in front of the reciprocal. So for this problem, the reciprocal is 1/1 = 1. The perpendicular slope is -1. So that is half the battle, we now have m = -1.

Next we are going to use the given point to solve for the intercept.

(x,y) = (3, -2) so

y = m x + b

-2 = -1 (3) + b

-2 = -3 + b

+3 +3

1 = b

So the intercept is equal to 1. Lastly, we take these two pieces of information that we have solved for (slope and intercept) and put them together. The answer is:

y = -1 x + 1

-1 times x just equals -x though, so we arrive at

y = -x + 1