Question

Which unit rate corresponds to the proportional relationship shown in the graph?

Drag and drop the answer into the box to match the graph with its unit rate.
A graph with a line running through coordinates left parenthesis 0 comma 0 right parenthesis and coordinates left parenthesis 6 comma 9 right parenthesis.
​0.33 cm/s​​0.5 cm/s​​0.67 cm/s​​1.5 cm/s​

Answer 1

1.5 cm/s​

Explanation:

The unit rate is the same as the slope.

To find the slope, we use the slope formula:

`m=(y_2-y_1)/(x_2-x_1)`

Using our points, we have

m = (9-0)/(6-0) = 9/6 = 3/2 = 1.5 cm/s

Answer 2

Equation of line having coordinates
`(x_(1),y_(1)), (x_(2),y_(2)) {\text{is given by two point formula for line}} = (y-y_(1))/(x-x_(1))= (y_(2)-y_(1))/(x_(2)-x_(1))`

Now,as given the line passes through (0,0) and (6,9).

So, equation of line passing through (0,0) and (6,9) is :

→
`(y-0)/(x-0)=(9-0)/(6-0)\\\\ y=(9)/(6) * x \\\\ y= 1.5 x`

As , slope intercept form of line is , y = m x +c

By comparing two lines

we get, m = 1.5

We can also find directly slope of line using the formula

m=
`(y_(2)-y_(1))/(x_(2)-x_(1))=(9-0)/(6-0)=1.5`cm/s→→option (D)