Question

The graphs of y = f(x) and y = g(x) are shown on the coordinate plane below. If g(x) = k* f(x), what is the value of k?

Answer 1

Answer:

Value of k = -2

Step-by-step explanation:

Using slope intercept form:

The equation of line is given by:

y = mx+b

where, m is the slope and b is the y-intercept.

As per the statement:

The graphs of y = f(x) and y = g(x) are shown on the coordinate plane.

First find f(x):

Consider two points on y=f(x) are:

(0,-3) and (2, 1)

Formula for slope:

$\text{Slope(m)} = \frac{y_2-y_1}{x_2-x_1}$

then;

$m = \frac{1-(-3)}{2-0}=\frac{4}{2} = 2$

then;

$y = 2x+b$

Substitute the point (0, -3) to solve for b:

$-3= 2(0)+b$

⇒$-3=b$

∴ $y=f(x)=2x-3$

Similarly for g(x):

Consider two points on y = g(x) are:

(0, 6) and (2, -2)

then;

$\text{Slope(m)} = \frac{y_2-y_1}{x_2-x_1}$

then;

$m = \frac{-2-6}{2-0}=\frac{-8}{2} =-4$

then;

$y = -4x+b$

Substitute the points (0, 6) to solve for b:

$6= -4(0)+b$

⇒$6=b$

then we get an equation:

y = g(x) = -4x+6

It is given that: If g(x) = k* f(x)

Solve for k:

$-4x+6 = k(2x-3)$

⇒$-4x+6 = 2kx-3k$

on comparing both sides we have;

$-2kx = -4x$

⇒$-2k = -4$

Divide both sides by -2 we have;

$k = 2$

or

-3k = 6

⇒k = -2

Therefore, the value of k is, -2

Answer 2

Consider this option:
1. according to the attached graph the equation for line f is f(x)=2x-3 (it is easy to determine it using coordinates of points (0;-3) and (2;1));
2. according to the graph the equation for line g is g(x)=-4x+6 (using coordinates of points (0;6) and (2;-2)).
3. according to the condition g(x)=k*f(x), k=g(x)/f(x)=(-4x+6)/(2x+3)=-2.

answer: -2