Question

Below are two different functions, f(x) and g(x). What can be determined about their slopes?

Answer 1

Answer:

C. They both have the same slope.

Step-by-step explanation:

We have the function f(x) = 3x-3.

Substituting values of x in above f(x), we get the pair of points (0,-3) and (1,0).

Now, we will find the slope m of this function using,

$m = \frac{y_{2} -y_{1} }{x_{2}- x_{1} }$

i.e. $m = \frac{0 - (-3)}{1-0}$

i.e. m = 3.

Now, we are given that the function g(x) passes through the points (0,2) and (1,5).

We will find the slope of g(x) also by using the formula above,

i.e. $m = \frac{5 - 2}{1-0}$

i.e. m = 3.

Hence, we can see that both f(x) and g(x) have slope 3.

So, they both have same slope.

Answer 2

Let's find the slope of the line through (0,2) and (1,5)

m = (y2 - y1)/(x2 - x1)
m = (5-2)/(1-0)
m = 3/1
m = 3

So the slope of g(x) is 3. The slope of f(x) is also 3. The two functions have the same slope.