Question

8.EE.5
Identify the unit rate of the proportional relationships

Answer 1

3.)
`3`

4.)
`(1)/(2)`

5.)
`40`

6.)
`15`

7.)
`8.25`

Explanation:

3.)
`5y=15x`

Solve for y and convert to slope-intercept form:

Isolate the variable, y, by dividing both sides by 5:

`(5y)/(5)=(15x)/(5)\\\\ y=3x`

This can be seen as:

`y=3x+0`

The slope is
`3`.

4.)
`8y=4x`

Solve for y and convert to slope-intercept form:

Isolate the variable y by dividing both sides by 8:

`(8y)/(8) =(4x)/(8) \\\\y=(1)/(2)x`

This can be seen as:

`y=(1)/(2) x+0`

The slope is
`(1)/(2)`.

5-7:

When you are given coordinate points, use the slope formula:

`(x_(1),y_(1))\\\\(x_(2),y_(2))\\\\(y_(2)-y_(1))/(x_(2)-x_(1)) =slope`

5.) Take two points:

`(1,40)(2,80)`

Insert into the slope formula:

`(80-40)/(2-1)= (40)/(1)=40`

The slope is
`40`.

6.) Take two points:

`(2,30)(4,60)`

Insert into the slope formula:

`(60-30)/(4-2) =(30)/(2) =15`

The slope is
`15`.

7.) Take two points:

`(5,41.25)(10,82.50)`

Insert into the slope formula:

`(82.50-41.25)/(10-5)=(41.25)/(5) =8.25`

The slope is
`8.25`.

Answer 2

1.)
`(2)/(3)`

2.)
`7`

Explanation:

1-4:

When given an equation, it is usually better to rewrite it in slope-intercept form:

`y=mx+b`

Where:

• m is the slope
• b is the y-intercept (when x is equal to 0)
• and x and y are the corresponding points (x,y)

1.)
`y=(2)/(3)x`

This is written in slope-intercept form as:

`y=(2)/(3)x+0`

The slope is
`(2)/(3)`.

2.)
`y=7x`

This is written in slope-intercept form as:

`y=7x+0`

The slope is
`7`.