Question

Choose the function that represents the data in the table.

A.Y= 0.5x^2+6
B. Y= 0.5^x+6
C. Y= 0.5x+ 6
D. Y= x^0.5+ 6

Answer 1

Given:

It is given that the function represents the data in the table.

We need to determine the function.

Slope:

The slope can be determined using the formula,

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

Let us substitute the coordinates (1,6.5) and (4,8) in the above formula, we get;

`m=(8-6.5)/(4-1)`

`m=(1.5)/(3)`

`m=0.5`

Thus, the slope is 0.5

y - intercept:

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

Thus, from the table, when x = 0 the corresponding y value is 6.

Therefore, the y - intercept is
`b=6`

Equation of the function:

The equation of the function can be determined using the formula,

`y=mx+b`

Substituting the values
`m=0.5` and
`b=6`, we get;

`y=0.5x+6`

Thus, the equation of the function is
`y=0.5x+6`

Hence, Option C is the correct answer.