Question

(01.06) Below are two different functions, f(x) and g(x). What can be determined about their slopes? f(x)= 3x − 3 The function g(x) going through 0, 2 and 1, 5 (1 point) The function f(x) has a larger slope. The function g(x) has a larger slope. They both have the same slope. The relationship between slopes cannot be determined.

Answer 1

Answer:

They both have the same slope

Step-by-step explanation:

The standard equation of a given line is expressed as y = mx+c where m is the slope and c is the intercept.

given the function f(x)= 3x − 3, comparing this equation with the standard format, we will have;

mx = 3x

Divide through by x

mx/x = 3x/x

m = 3

Hence the slope of the function f(x)= 3x − 3 is 3.

For a function g(x) passing through the points (0, 2) and (1, 5), to determine the slope, we will use the formula for calculating slope expressed as;

m = Δy/Δx = y₂-y₁/x₂-x₁

From the coordinates, x₁ = 0, y₁ = 2, x₂ = 1, y₂ = 5

m = 5-2/1-0

m = 3/1 = 3

Hence the slope of g(x) passing through the points (0, 2) and (1, 5) is also 3.

This shows that both functions have the same slope.