Question

For a given function, the graph of x and y is shown below. Which of the following statements are true? Check all that apply.

graph on coordinate plane, line passing through points (negative 4, negative 2), (negative 2, negative 1), (0, 0), (2, 1), (4, 2), and beyond



The variable y varies directly with x.


The constant of variation is .


The constant of variation is 2.


The variable y does not vary directly with x.

Answer 1

I think thats right.

Answer 2

Explanation:

Given that line passes through (0,0) and (2,1)

(Note that any two points are sufficient to determine the equation of the line)

The slope = change in y/change in x = (1-0)/(2-0) = 1/2

Hence answers are:

Variable y varies directly with x. (if x increases y also increases and vice versa)

The constant of variation = slope of line = 1/2

The constant of variation is 2 is wrong since slope = 1/2

The variable y does not vary directly with x is wrong since when x increases by 1 unit y increases by 1/2 unit for all real x.