Question

Based on the graph, which equation represents the relationship between the height of trees (y) and the amount of rainfall (x)?

A. height of trees (y) × 0.5 = amount of rainfall (x)
B. height of trees (y) = 10 + amount of rainfall (x)
C. height of trees (y) = 0.5 × amount of rainfall (x)
D. height of trees (y) = 5 × amount of rainfall (x)

Answer 1

C. height of trees (y) = 0.5 × amount of rainfall (x)

Explanation:

y - intercept = 0

Slope: (10-0)/(20-0) = ½

Answer 2

Given:

Given that the graph that shows the amount of rainfall( in centimeters) and the height of the trees( in meters)

We need to determine the equation that represents the relationship between the height of trees(y) and the amount of rainfall(x).

Slope of the equation:

The slope can be determined using the formula,

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

Substituting the points (20,10) and (40, 20) in the above formula.

Thus, we get;

`m=(20-10)/(40-20)`

`m=(10)/(20)`

`m=0.5`

Thus, the slope of the equation is 0.5

y - intercept:

The y - intercept of the equation is the value of y when x = 0.

Thus, from the graph, when x = 0, the value of y is 0.

Hence, the y - intercept is b = 0

Equation of the graph:

The equation of the given graph can be determined using the formula,

`y=mx+b`

Substituting the values, we get;

`y=0.5x+0`

`y=0.5x`

Thus, the equation that represents the relationship between the height of the trees (y) and the amount of rainfall (x) is
`y=0.5x`

Hence, Option C is the correct answer.