SOLUTION: passing through 0,4 perpendicular to -7y+x-8=0

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Question 1124208: passing through 0,4 perpendicular to -7y+x-8=0
Found 2 solutions by MathLover1, MathTherapy:
Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!

passing through (0,4)
perpendicular to -7y%2Bx-8=0->x-8=7y->y=%281%2F7%29x-8%2F7

Solved by pluggable solver: Finding the Equation of a Line Parallel or Perpendicular to a Given Line


Remember, any two perpendicular lines are negative reciprocals of each other. So if you're given the slope of 1%2F7, you can find the perpendicular slope by this formula:

m%5Bp%5D=-1%2Fm where m%5Bp%5D is the perpendicular slope


m%5Bp%5D=-1%2F%281%2F7%29 So plug in the given slope to find the perpendicular slope



m%5Bp%5D=%28-1%2F1%29%287%2F1%29 When you divide fractions, you multiply the first fraction (which is really 1%2F1) by the reciprocal of the second



m%5Bp%5D=-7%2F1 Multiply the fractions.


So the perpendicular slope is -7



So now we know the slope of the unknown line is -7 (its the negative reciprocal of 1%2F7 from the line y=%281%2F7%29%2Ax%2B8%2F7). Also since the unknown line goes through (0,4), we can find the equation by plugging in this info into the point-slope formula

Point-Slope Formula:

y-y%5B1%5D=m%28x-x%5B1%5D%29 where m is the slope and (x%5B1%5D,y%5B1%5D) is the given point



y-4=-7%2A%28x-0%29 Plug in m=-7, x%5B1%5D=0, and y%5B1%5D=4



y-4=-7%2Ax%2B%287%29%280%29 Distribute -7



y-4=-7%2Ax-0 Multiply



y=-7%2Ax-0%2B4Add 4 to both sides to isolate y

y=-7%2Ax%2B4 Combine like terms

So the equation of the line that is perpendicular to y=%281%2F7%29%2Ax%2B8%2F7 and goes through (0,4) is y=-7%2Ax%2B4


So here are the graphs of the equations y=%281%2F7%29%2Ax%2B8%2F7 and y=-7%2Ax%2B4




graph of the given equation y=%281%2F7%29%2Ax%2B8%2F7 (red) and graph of the line y=-7%2Ax%2B4(green) that is perpendicular to the given graph and goes through (0,4)

Answer by MathTherapy(10551) About Me  (Show Source):
You can put this solution on YOUR website!

passing through 0,4 perpendicular to -7y+x-8=0
- 7y + x - 8 ======> x - 7y = 8

If of the form: Ax - By, and perpendicular, then the perpendicular form is: Bx + Ay 

Therefore, x - 7y = 8 becomes: 7x + y = c, with c = 7 * x + y

We then get: 7x + y = 7(0) + 4

Equation: highlight_green%28matrix%281%2C3%2C+7x+%2B+y%2C+%22=%22%2C+4%29%29

That's ALL that is there to it!!