Question

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

Answer 1

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
`( x_(1) , y_(1) )` and another
`( x_(2) , y_(2) )`. 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:

`( x_(1) , y_(1) )= (0.0)`

`( x_(2) , y_(2) )= (1.3)`

The slope formula is:
`m= (y_(2) - y_(1) )/( x_(2)- x_(1) )`
We now substitute the values we got from the points to obtain.

`m= (3-0)/( 1-0 ) = (3)/(1)=3`

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