MATH SOLVE

4 months ago

Q:
# 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

Accepted Solution

A:

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 [tex]( x_{1} , y_{1} )[/tex] and another [tex]( x_{2} , y_{2} )[/tex]. 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:

[tex]( x_{1} , y_{1} )= (0.0)[/tex]

[tex]( x_{2} , y_{2} )= (1.3)[/tex]

The slope formula is: [tex]m= \frac{y_{2} - y_{1} }{ x_{2}- x_{1} } [/tex]

We now substitute the values we got from the points to obtain.

[tex]m= \frac{3-0}{ 1-0 } = \frac{3}{1}=3 [/tex]

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

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 [tex]( x_{1} , y_{1} )[/tex] and another [tex]( x_{2} , y_{2} )[/tex]. 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:

[tex]( x_{1} , y_{1} )= (0.0)[/tex]

[tex]( x_{2} , y_{2} )= (1.3)[/tex]

The slope formula is: [tex]m= \frac{y_{2} - y_{1} }{ x_{2}- x_{1} } [/tex]

We now substitute the values we got from the points to obtain.

[tex]m= \frac{3-0}{ 1-0 } = \frac{3}{1}=3 [/tex]

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