Help with parallel and perpendicular lines?

Question

My math packet didn't give examples for this part so can you help me?

Tell which of the given equations have parallel line graphs and which have perpendicular line graphs:

1. y=5/2x - 8

2. -15x + 6y - 10=10

3. 4x + 10y = 15

4. 2x + 3y = 1

5. y= 3/2x + 3

6. 6x - 4y -10 = 0

Answer 1

Parallel lines have the same slope. Perpendicular lines have slopes that are negative inverses (example: 2/3 and -3/2).

1. y = (5/2)x - 8

slope = 5/2

2. -15x+6y-10 = 10

6y = 15x+20

y = (5/2)x+10/3

slope = 5/2

3. 4x + 10y = 15

10y = -4x + 15

y = (-2/5)x + 3/2

slope = -2/5

4. 2x + 3y = 1

3y = -2x + 1

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

slope = -2/3

5. y = (3/2)x + 3

slope = 3/2

6. 6x - 4y - 10 = 0

4y = 6x-10

y = (3/2)x - 5/2

slope = 3/2

Equations 1 and 2 have parallel line graphs.

Equation 3 has a line graph perpendicular to the graphs of equations 1 and 2.

Equations 5 and 6 have parallel graphs.

Equation 4 has a graph perpendicular to the graphs of equations 5 and 6.

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Answer 2

Get them all into slope-intercept form:

1. y=(5/2)x-8

2. 6y=15x+20 or y=(5/2)x+10/3

3. 10y=-4x+15 or y=(-2/5)x+3/2

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

5. y=(3/2)x+3

6 -4y=-6x+10 or y=(-3/2)x-5/2

1 and 2 have the same slope, so they are parallel

1 and 3, 2 and 3 are perpendicular because if you multiply their slopes the result is -1

4 and 5 are perpendicular because if you multiply their slopes the result is -1

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