Question

Write the slope-intercept equation for the line that passes through (8, 12) and is perpendicular to -4x – 7y = 14
Please show all of your work.

Answer 1

Ok, so remember that Slope-Intercept looks like this: y=mx+b
And perpendicular is the negative inverse of your slope.
But first, lets get this baby is y=mx+b
-4x-7y=14 (Trick is to get y by its self)
+4x +4x (Move the x to other side.)
-7y=4x+14
/-7 /-7 /-7 (Divide everything by -7)
y=-4/7x -2
Ok, so we have that, but now we're only half done. Now you put the perpendicular version of your new found slope (-4/7) which will be (7/4). Remember it's positive now because it's the reciprocal of your last slope.
This is where your point (8,12) come in to play. Remember that x=8 and y=12. So plug these into your equation for x and y, leaving the y-intercept blank. The y-intercept it what you're going to find for the final answer.
Here we go:
y=7/4x+b (Put in perpendicular version of your slope, leave y-intercept blank)
12=7/4(8)+b (Add in your points for x & y. Now we're going to solve for b)
12=14+b (Multiply)
-14 -14 (Minus 14 to get b)
-2=b (And there is our y-intercept!)
Now just plug in your perpendicular slope and the y-intercept we just found
y=7/4x-2 (That's the answer! Be sure it follows the y=mx+b)