Question

PLZ HELP!!!!!!!! due in 30 minutes im timed!

Answer 1

Option D:

Difference between g(x) and f(x) is 44.

Solution:

Let us first write the function of f(x).

Take any two points on the line (0, -1) and (-2, 0).

Here, $x_1=0, y_1=-1, x_2=-2, y_2=0$

Equation of a line:

$\frac{y-y_1}{x-x_1} =\frac{y_2-y_1}{x_2-x_1}$

$\frac{y-(-1)}{x-0} =\frac{0-(-1)}{-2-0}$

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

Do cross multiplication.

-2(y + 1) = x

-2y - 2 = x

Add 2 on both sides.

-2y = x + 2

Divide by -2 on both sides.

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

y = -0.5x - 1

f(x) = -0.5x - 1

At x = 20,

f(20) = -0.5(20) - 1 = -11

g(x) = 1.5x + 3

g(20) = 1.5(20) + 3 = 33

Difference between g(x) and f(x)

            = g(20) - f(20)

            = 33 - (-11)

            = 33 + 11

            = 44

Difference between g(x) and f(x) is 44.

Option D is the correct answer.