# 3.04 Equations of parallel and perpendicular lines

## Interactive practice questions

The equations $y=2x$y=2x, $y=2x+6$y=2x+6 and $y=2x-8$y=2x8 have been graphed on the same number plane:

a

What do all of the equations have in common?

Their $y$y-intercept ($b$b)

A

Their slope ($m$m).

B

Their $x$x-intercept.

C

Their $y$y-intercept ($b$b)

A

Their slope ($m$m).

B

Their $x$x-intercept.

C
b

What do you notice about the graphs?

All graphs cut the $y$y-axis at the same point.

A

All graphs cut the $x$x-axis at the same point.

B

All graphs have the same angle of inclination.

C

All graphs cut the $y$y-axis at the same point.

A

All graphs cut the $x$x-axis at the same point.

B

All graphs have the same angle of inclination.

C
c

What can you conclude from the answers above?

Equations with the same $x$x-intercept have graphs that have the same angle of inclination.

A

Equations with the same slope ($m$m) cut the $y$y-axis at the same point.

B

Equations with the same slope ($m$m) have graphs that have the same angle of inclination.

C

Equations with the same $y$y-intercept ($b$b) have graphs that have the same angle of inclination.

D

Equations with the same $x$x-intercept have graphs that have the same angle of inclination.

A

Equations with the same slope ($m$m) cut the $y$y-axis at the same point.

B

Equations with the same slope ($m$m) have graphs that have the same angle of inclination.

C

Equations with the same $y$y-intercept ($b$b) have graphs that have the same angle of inclination.

D
Easy
Approx a minute

Is the line $y=4x-1$y=4x1 parallel to $y=4x-6$y=4x6 ?

Is the line $y=-8x-2$y=8x2 parallel to $y=9x+7$y=9x+7 ?

Are the lines $y=-6x-5$y=6x5 and $y=x$y=x parallel?

### Outcomes

#### GEO-G.GPE.5a

On the coordinate plane, explore the proof for the relationship between slopes of parallel and perpendicular lines;

#### GEO-G.GPE.5b

On the coordinate plane, determine if lines are parallel, perpendicular, or neither, based on their slopes;

#### GEO-G.GPE.5c

On the coordinate plane, apply properties of parallel and perpendicular lines to solve geometric problems.