Question

Find the equation of a line perpendicular to y - 12 = 2x – 8 that passes through the point (2, 3). (answer in slope-intercept form)

Answer 1

Answer:

The equation of the line would be y = -1/2x + 4

Step-by-step explanation:

In order to find a perpendicular line, start by finding the equation for this line. To do so, solve for y.

y - 12 = 2x - 8

y = 2x + 4

Now that we have this, we know the slope is 2. Since we are looking for a perpendicular line, we take the opposite and reciprocal, which gives out new line a slope of -1/2. We can use this and the point in point-slope form to find the equation.

y - y1 = m(x - x1)

y - 3 = -1/2(x - 2)

y - 3 = -1/2x + 1

y = -1/2x + 4

Answer 2

First, we can add 12 to both sides to get..
y=2x+4 
To get a perpendicular line, we have to take the reciprocal of the current slope and turn it to the opposite sign (ex: if it is positive, make it negative, if it is negative, make it positive) 
y= -(1/2)x+4
To make sure it passes through the points (2,3) we substitute x=2 and y=3 (x,y) 
3= -(1/2)2 +4
3= (-1) + 4
3=3
Now we know the equation is working
y= -(1/2)x + 4