Question

Graph the line that represents a proportional relationship between d and t with the property that and increase of 0.2 units in t corresponds to an increase of 1.8 units in d.

What is The unit rate of change is d with respect to t? (This is, a change of 1 unit in t will correspond to a change of how many units in d?)

The unit rate of change is
____________.

Answer 1

The unit rate of change is 9 units.

Explanation:

We have to draw a line which represents a proportional relationship between d and t. In the graph t is represented on x-axis represents and d is represent on y-axis.

It is given that increase of 0.2 units in t corresponds to an increase of 1.8 units in d.

The unit rate of change is also known as slope.

`Slope=\frac{\text{Change in y}}{\text{Change in x}}`

For the given case,

`Slope=\frac{\text{Change in d}}{\text{Change in t}}`

`Slope=(1.8)/(0.2)`

`Slope=9`

Therefore the unit rate of change is 9 units.

There is a proportional relationship between d and t, therefore the line must be passing through (0,0).

The point slope form of a line

`y-y_1=m(x-x_1)`

Where m is the slope.

`y=9x`

Therefore the equation of line is
`y=9x`.