Question

Ishwar pours sand into a bucket at a constant rate. The graph shows the total weight of the bucket and the sand over time. After 10 seconds, the total weight is 50 ounces. What is an equation of the line parallel to the line on the graph that passes through (4, 15)?

Answer 1

Option C.

Explanation:

If a line passes through two points
`(x_1,y_1)` and
`(x_2,y_2)`, then the rate of change is

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

From the given graph it is clear that the line passes through the points (0,20) and (10,50). So, the slope of the lien is

`m=(50-20)/(10-0)=(30)/(10)=3`

The slope of two parallel lines are same. So, the slope of parallel line is 3.

The point slope form of a line is

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

The slope of parallel line is 3 and it passes through the point (4,15). So, the equation of parallel line is

`y-15=3(x-4)`

Using distributive property

`y-15=3x-12`

Add 15 on both sides.

`y=3x-12+15`

`y=3x+3`

The required equation is y=3x+3. Therefore, the correct option is C.