Question

determine whether 3x-5y=11 and 15x+9y=10 are parallel perpendicular or neither

Answer 1

if slopes are equal ,lines are parallel.
if their product is -1,lines are perpendicular.

Answer 2

14y + 5x + 7 = 5 + 5x

Subtract 5x on both sides

14y+7=5

Subtract 5 on both sides

14y=-2

Divide 14 on both sides

y=-1/7

So the slope is 0 and the y intercept is -1/7

2)3x - 5y + 5 = 0

Subtract 3x on both sides

-5y+5=-3x

Subtract 5 on both sides

-5y=-3x-5

Divide -5 to everything

y=(3/5)x+1

So slope is 3/5 and y-intercept is 1

3) 3x - 4y = -15
8x + 6y = -15

Put them both in slope-intercept form. Parallel lines have same slope, perpendicular lines have negative reciprocal slopes, and neither has neither.

3x-4y=-15
-4y=-3x-15
y=(3/4)x+(15/4)

Slope is 3/4

8x+6y=-15
6y=-8x-15
y=(-4/3)x-(5/2)

Slope is -4/3. So they are perpendicular

4)3x - 4y = -8
8x + 6y = -8

3x-4y=-8
-4y=-3x-8
y=(3/4)x+2

8x+6y=-8
6y=-8x-8
y=(-4/3)x-(4/3)

They are perpendicular

5) y + 18 = -4x
6y = 36x - 12

y+18=-4x
y=-4x-18

6y=36x-12
y=6x-2

Neither

6)4x - 2y = -15
4x + 3y = -15

4x-2y=-15
-2y=-4x-15
y=2x+(15/2)

4x+3y=-15
3y=-4x-15
y=(-4/3)x-5

neither

7)12x + 4y = 16
15x + 5y = 24

12x+4y=16
4y=-12x+16
y=-3x+4

15x+5y=24
5y=-15x+24
y=-3x+(24/5)

Parallel

8) 9x + 3y = 12
12x + 4y = 19

3y=-9x+12
y=-3x+4

4y=-12x+19
y=-3x+(19/4)

Parallel

9) 3x=-8
9y=-8

x=-8/3

Slope is undefined

y=-8/9

Slope is 0

Perpendicular

10) (-4, -8) and (4, 1)

Find slope. Slope is change in y divided by change in x

(1--8)/(4--4)

9/8

Put in slope-intercept form

y=mx+b
y=(9/8)x+b

To find b, substitute in one of the ordered pairs

-8=(9/8)(-4)+b
-8=-9/2+b
-7/2=b

So:

y=(9/8)x-(7/2)

Answer 3

means product of slopes