The table below represents a linear function in the equation represents a function. table numbers are x: -1,0,1. f(x): -3,0,3. g(x): g(x) = 7x + 2 part a: write a sentence to compare the slope of the two functions and show the steps used to determine the slope of fx and gx. part b: which function has a greater y intercept? justify your answer

A)
SLOPE OF f(x)
To find the slope of f(x) we pick two points on the function and use the slope formula. Each point can be written (x, f(x) ) so we are given three points in the table. These are: (-1, -3) , (0,0) and (1,3). We can also refer to the points as (x,y). We call one of the points and another . It doesn't matter which two points we use, we will always get the same slope. I suggest we use (0,0) as one of the points since zeros are easy to work with.

Let's pick as follows:



The slope formula is:
We now substitute the values we got from the points to obtain.


The slope of f(x) = 3

SLOPE OF g(x)
The equation of a line is y=mx+b where m is the slope and b is the y intercept. Since g(x) is given in this form, the number in front of the x is the slope and the number by itself is the y-intercept.

That is, since g(x)=7x+2 the slope is 7 and the y-intercept is 2.

The slope of g(x) = 2

B)
Y-INTERCEPT OF g(x)
From the work in part a we know the y-intercept of g(x) is 2.

Y-INTERCEPT OF f(x)
The y-intercept is the y-coordinate of the point where the line crosses the y-axis. This point will always have an x-coordinate of 0 which is why we need only identify the y-coordinate. Since you are given the point (0,0) which has an x-coordinate of 0 this must be the point where the line crosses the y-axis. Since the point also has a y-coordinate of 0, it's y-intercept is 0

So the function g(x) has the greater y-intercept