SOLUTION: HELP HELP HELP.....PLEASE PLEASE Question 1: Write equation of the line containing the given point and parallel to the given line y=mx+b: A. (5,7) x + 7y =5 The equation li

Algebra ->  Algebra  -> Finance -> SOLUTION: HELP HELP HELP.....PLEASE PLEASE Question 1: Write equation of the line containing the given point and parallel to the given line y=mx+b: A. (5,7) x + 7y =5 The equation li      Log On

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Question 146634: HELP HELP HELP.....PLEASE PLEASE
Question 1: Write equation of the line containing the given point and parallel to the given line y=mx+b:
A. (5,7) x + 7y =5 The equation line is y???
B. (-9,5)4x =5y + 7 The equation line is y???
Question 2: Write equation of a line containing given point and perpendicular to given line.
A. Express answer y=mx+b (3,6); 8x + y = 9 The equation of the line is y???
B. (2,-6); 8x +3y =3 The equation of the line is y???
Found 2 solutions by jim_thompson5910, scott8148:
Answer by jim_thompson5910(21667) About Me  (Show Source):
You can put this solution on YOUR website!
I'll do one of each to get you started

1)

A)



x+%2B+7y+=5 Start with the given equation.


y=-%281%2F7%29x%2B5%2F7 Solve for y.


We can see that the equation y=-%281%2F7%29x%2B5%2F7 has a slope m=-1%2F7 and a y-intercept b=5%2F7.


Since parallel lines have equal slopes, this means that we know that the slope of the unknown parallel line is m=-1%2F7.
Now let's use the point slope formula to find the equation of the parallel line by plugging in the slope m=-1%2F7 and the coordinates of the given point .


y-y%5B1%5D=m%28x-x%5B1%5D%29 Start with the point slope formula


y-7=%28-1%2F7%29%28x-5%29 Plug in m=-1%2F7, x%5B1%5D=5, and y%5B1%5D=7


y-7=%28-1%2F7%29x%2B%28-1%2F7%29%28-5%29 Distribute


y-7=%28-1%2F7%29x%2B5%2F7 Multiply


y=%28-1%2F7%29x%2B5%2F7%2B7 Add 7 to both sides.


y=%28-1%2F7%29x%2B54%2F7 Combine like terms. note: If you need help with fractions, check out this solver.


So the equation of the line parallel to x+%2B+7y+=5 that goes through the point is y=%28-1%2F7%29x%2B54%2F7.


Here's a graph to visually verify our answer:
drawing%28500%2C+500%2C+-10%2C+10%2C+-10%2C+10%2C%0D%0Agraph%28500%2C+500%2C+-10%2C+10%2C+-10%2C+10%2C-%281%2F7%29x%2B5%2F7%2C%28-1%2F7%29x%2B54%2F7%29%2C%0D%0Acircle%285%2C7%2C0.08%29%2C%0D%0Acircle%285%2C7%2C0.10%29%2C%0D%0Acircle%285%2C7%2C0.12%29%29Graph of the original equation y=-%281%2F7%29x%2B5%2F7 (red) and the parallel line y=%28-1%2F7%29x%2B54%2F7 (green) through the point .







2)

A)




8x+%2B+y+=+9 Start with the given equation.


y=-8%2Ax%2B9 Solve for y.


We can see that the equation y=-8%2Ax%2B9 has a slope m=-8 and a y-intercept b=9.


Now to find the slope of the perpendicular line, simply flip the slope m=-8 to get m=-1%2F8. Now change the sign to get m=1%2F8. So the perpendicular slope is m=1%2F8.


Now let's use the point slope formula to find the equation of the perpendicular line by plugging in the slope m=-8 and the coordinates of the given point .


y-y%5B1%5D=m%28x-x%5B1%5D%29 Start with the point slope formula


y-6=%281%2F8%29%28x-3%29 Plug in m=1%2F8, x%5B1%5D=3, and y%5B1%5D=6


y-6=%281%2F8%29x%2B%281%2F8%29%28-3%29 Distribute


y-6=%281%2F8%29x-3%2F8 Multiply


y=%281%2F8%29x-3%2F8%2B6 Add 6 to both sides.


y=%281%2F8%29x%2B45%2F8 Combine like terms. note: If you need help with fractions, check out this solver.


So the equation of the line perpendicular to 8x+%2B+y+=+9 that goes through the point is y=%281%2F8%29x%2B45%2F8.


Here's a graph to visually verify our answer:
drawing%28500%2C+500%2C+-10%2C+10%2C+-10%2C+10%2C%0D%0Agraph%28500%2C+500%2C+-10%2C+10%2C+-10%2C+10%2C-8%2Ax%2B9%2C%281%2F8%29x%2B45%2F8%29%0D%0Acircle%283%2C6%2C0.08%29%2C%0D%0Acircle%283%2C6%2C0.10%29%2C%0D%0Acircle%283%2C6%2C0.12%29%29Graph of the original equation y=-8%2Ax%2B9 (red) and the perpendicular line y=%281%2F8%29x%2B45%2F8 (green) through the point .

Answer by scott8148(5880) About Me  (Show Source):
You can put this solution on YOUR website!
"HELP HELP HELP.....PLEASE PLEASE" __ not too panicky...

parallel lines have the same slope
perpendicular lines have slopes which are negative reciprocals

1.A. subtracting x __ 7y=-x+5 __ dividing by 7 __ y=(-1/7)x+(5/7) __ new slope is -1/7
__ using point-slope __ y-7=(-1/7)(x-5) __ y=(-1/7)x+(54/7)

1.B. subtracting 7 __ 5y=4x-7 __ dividing by 5 __ y=(4/5)x-(7/5) __ new slope is 4/5
__ using point-slope __ y-5=(4/5)(x+9) __ y=(4/5)x+(34/5)

2.A. subtracting 8x __ y=-8x+9 __ new slope is 1/8
__ using point-slope __ y-6=(1/8)(x-3) __ y=(1/8)x+(45/8)

2.B. subtracting 8x __ 3y=-8x+3 __ dividing by 3 __ y=(-8/3)x+1 __ new slope is 3/8
__ using point-slope __ y+6=(3/8)(x-2) __ y=(3/8)x-(27/4)