The table below shows the values of y for different values of x:
x y
0
0
1
5
2
10
3
15
which equation shows the relationship between x and y?

Step-by-step explanation:

we know that

A relationship between two variables, x, and y, represent a proportional variation if it can be expressed in the form or

In a proportional relationship the constant of proportionality k is equal to the slope m of the line and the line passes through the origin

we have

For x=0, y=0 -----> the line passes through the origin

For x=1, y=5 ---->

For x=2, y=10 ---->

For x=3, y=15 ---->

so

The constant of proportionality is k=5

The table represent a direct variation

The equation is equal to

substitute the value of k

y=1/4x-4

step-by-step explanation:

1 number

if we use a graphing calculator, there is only one such number that satisfies the conclusion of the mean value theorem, that is, a number such that

where the right-hand side is the average rate of change of f on the interval [0.5,0.75], which is the slope of the secant line.

in the attached graph, the black line is the secant line which has its slope as the average rate of change of f on [0.5,0.75], while the orange line is the only tangent line to the graph of f in the interval that satisfies the mvt conclusion.