Question

The table shows a linear function. which equation represents the function?

Answer 1

Answer:

Option C is correct.

The equation $f(x)= -\frac{1}{2}x +4$ represents the function.

Step-by-step explanation:

Using slope intercept form to find the equation of line :

For any two points $(x_1, y_1)$ and  $(x_2, y_2)$ the equation of line is given by:

$y -y _1 = m(x-x_1)$ ......[1] ;where m is the slope given by:

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

Consider any two points from table :

let (4, 2) and (0, 4) be any two points.

calculate slope:

$m = \frac{y_2-y_1}{x_2-x_1}= \frac{4-2}{0-4}$

$m = \frac{2}{-4} = -\frac{1}{2}$

Now, substitute in equation [1]  we have:

$y - 2 = -\frac{1}{2} (x-4)$

Distributive property i.e,  $a\cdot (b+c) = a\cdot b + a\cdot c$

$y -2 = -\frac{1}{2}x +2$

Add both sides 2 we get;

$y -2+2 = -\frac{1}{2}x+2+2$

Simplify:

$y = -\frac{1}{2}x+4$

Since, y= f(x)

$f(x)= -\frac{1}{2}x +4$

therefore, the equation $f(x)= -\frac{1}{2}x +4$ represents the function.