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

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(35256) (Show Source): You can put this solution on YOUR website!
I'll do one of each to get you started

1)

A)

Start with the given equation.

Solve for y.

We can see that the equation has a slope and a y-intercept .

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

Start with the point slope formula

Plug in , , and

Distribute

Multiply

Add 7 to both sides.

Combine like terms. note: If you need help with fractions, check out this solver.

So the equation of the line parallel to that goes through the point is .

Here's a graph to visually verify our answer:
Graph of the original equation (red) and the parallel line (green) through the point .

2)

A)

Start with the given equation.

Solve for y.

We can see that the equation has a slope and a y-intercept .

Now to find the slope of the perpendicular line, simply flip the slope to get . Now change the sign to get . So the perpendicular slope is .

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

Start with the point slope formula

Plug in , , and

Distribute

Multiply

Add 6 to both sides.

Combine like terms. note: If you need help with fractions, check out this solver.

So the equation of the line perpendicular to that goes through the point is .

Here's a graph to visually verify our answer:
Graph of the original equation (red) and the perpendicular line (green) through the point .

Answer by scott8148(6628) (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)
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