Verified answer

Parallel:

2y=6-x

y=3-(1/2)x

y=-(1/2)x +c

3=-(1/2)(8)+c

c=7

So here is the equation: y=(-1/2)x +7

Perpendicular : You'll do the same for perp line, except the slope are opposite. y=(1/2)x+7

1) Rewrite the equation you have been given into x=mx + b format. In that form, m = slope and b = y-intercept.

x + 2y = 6

2y = -x + 6

y = (-1/2)x + 3

So, looking at the above, you can see that m = -1/2, so that is your slope.

A line that is parallel will have the same slope, so you know for the line you are trying to find, m = -1/2.

Use the following formula to find the equation of the line:

y - y1 = m(x - x1)

where m is the slope and x1 and y1 are a point (x1, y1) on the line (any point on the line that you know).

For this problem:

m = -1/2

(x1, y1) = (8,3)

Plug in the above values:

y - 3 = (-1/2)(x-8)

y - 3 = (-1/2)x - (-1/2)8

y - 3 = (-1/2)x + 4

y = (-1/2)x + 7

If you need to rearrange it into the same format as the equations in the question, do the following:

y = (-1/2)x + 7

(1/2)x + y = 7

2) Since we are using the same equation, we already know the slope of x+2y=6 is -1/2.

When a line is perpendicular to another, its slope will be the negative reciprocal of the other slope.

This means, to find the slope of the new line:

a) flip the fraction (eg: from 1/3 to 3/1)

b) switch signs (from positive to negative, or from negative to positive)

The first line's slope is -1/2.

The negative reciprocal is 2.

So, as in the first question, use the following formula and plug in your slope (m=2) and the point (8,3) to find the equation.

y - y1 = m(x - x1)

y - 3 = 2(x - 8)

y - 3 = 2x - 16

y = 2x - 13

I hope this helped!

PARALLEL

First find the slope

x + 2y = 6, passing through (8,3)

2y= -x+6 rewrite the equation into y=mx+b

divide both sides by 2

y= -1x/2+3

m= -1/2 and parallel lines have the same slope.

Second find b by substituting the 2 points given

x=8

y=3

3= -1/2(8)+b then solve

7=b

1st equation: y= -1x/2+7

PERPENDICULAR

x + 2y = 6, passing through (8,3)

2y= -x+6 rewrite the equation into y=mx+b

divide both sides by 2

y= -1x/2+3

m= -1/2 but the slope of perpendicular lines is the negative reciprocal.

where in m=2

Second find b by substituting the 2 points given

x=8

y=3

3= 2(8)+b then solve

-16+3=b

b=-13

2nd equation: y=2x-13

Got it?

hope it helps :-)

12x + 4y = 16 4y = 16 - 12x y = -3x + 4 slope m1 = -3 (y = mx + c) 5y - 22 = -15x y = -3x + 22/5 slope m2 = -3 thus, both lines are parallel to each other since they have same slope