Question

Write an equation of the line that passeg through (8, 1) and is perpendicular to the line 2y + 4x = 12

Answer 1

y=1/2x-3

Explanation:

First, let's put the line into slope intercept form

2y+4x=12

subtract 4x from both sides

2y=-4x+12

divide by 2

y=-2x+6

the slopes of perpendicular lines are negative and reciprocal. If you multiply the slopes of the lines together, the result is -1. Therefore, to find the slope of the perpendicular line, use this formula:

-2m=-1

divide by -2

m=1/2

so the slope of the perpendicular line is 1/2

here is the new line so far:

y=1/2x+b (b is a place holder)

now, since the line passes through the point (8,1), it means that (8,1) is a solution of the line. So we can substitute it into the equation

1=1/2(8)+b

1=4+b

subtract 4 from both sides

-3=b

so the line is y=1/2x-3

Hope this helps!