The table below represents a linear function f(x) and the equation represents a function g(x): Part A: Write a sentence to compare the slope of the two functions and show the steps you used to determine the slope of f(x) and g(x). (6 points)

Part B: Which function has a greater y-intercept? Justify your answer. (4 points)

Slope of f(x) is greater than slope of g(x)

g(x) has a greater y intercept

Step-by-step explanation:

Given

f(x) table

Solving (a):

First, we determine the slope of f(x).

From the table, we take any two corresponding values of x and f(x).

Represent f(x) with y

The slope (m) is calculated as thus

Represent this with m1

Calculating the slope of g(x).

The general form of an equation is

Where m represents the slope.

We have that:

By comparing   with

Represent this with m2

Comparing both slope, we can say that:

f(x) has a greater than slope of g(x)

Another comparison is that:

Slope of f(x) is 3 times the slope of g(x)

Solving (b): Function with greater y intercept.

The general form of an equation is

Where b represents the y intercept.

First, we need to determine the equation of f(x) using:

Recall that, from the table of f(x):

So:

Solve for y

By comparing this with , the y intercept of f(x) is -6

For g(x), we have:

By comparing this with , the y intercept of g(x) is 6

Comparing the y intercepts of both functions, g(x) has a greater y intercept because

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