Question

The foot of the perpendicular drawn from the point (2, 3) to a line is (3, -1). Find

the equation of the line. Also find the equation of the line parallel to the line and
passing through the origin.

Answer 1

Answer: y=4x-5 y=4x

Explanation:

first we find the slope by using

(y2-y1)/(x2-x1)

(-1-3)/(3-2)

-4/1

-4

so we know the slope is -4

y=4x+b

now we can use either point but ill use (2,3)

we substitute to find b

3=4(2)+b

3=8+b

-5=b

so now we know that the y intercept is -5

so put it together

y=4x-5

if it passes through the origin

it would have the y-intercept of 0

so that equation just be

y=4x

and it keeps the same slope

because they are parallel

hope this helped