Analytic Geometry

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

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a

What do all of the **equation**s 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

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Identify, through investigation, properties of the slopes of lines and line segments (e.g., direction, positive or negative rate of change, steepness, parallelism, perpendicularity), using graphing technology to facilitate investigations, where appropriate