Question

Choose the function that represents the data in the table.

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,

$m=\frac{y_2-y_1}{x_2-x_1}$

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

$m=\frac{8-6.5}{4-1}$

$m=\frac{1.5}{3}$

$m=0.5$

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.