Question

I don't just want the answer... I want help on how to figure this out... I don't understand it pleasssseeee I will give medals
The table below represents a linear function f(x) and the equation represents a function g(x):


x f(x)
−1 −9
0 −1
1 7
g(x)

g(x) = 3x − 2


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).

Answer 1

The slope of the line that passes through points \((x_1, y_1)\) and \((x_2, y_2)\) is

\(m = \dfrac{y_2 - y_1}{x_2 - x_1} \)

Answer 2

When the equation of a line is written in the slope-intercept form,

\(y = mx + b\),

m is the slope, and b is the y-coordinate of the y-intercept.

Answer 3

right i have that so far -1 -(-9) over 0-(-1) =8

Answer 4

To find the slope of function f(x), choose any to points from that function.
I see that you are using the points (-1, -9) and (0, -1).

\(m = \dfrac{-1 - (-9)}{0 - (-1)} = \dfrac{8}{1} = 8\)

You are correct. the slope of function f(x) is 8.

Now notice that function g(x) is written in the slope-intercept form, so you can read the slope right off the equation.
What is the slope of the function g(x)?

Answer 5

3

Answer 6

Correct.
The slope of f(x) is 8, and the slope of g(x) is 3.
That takes care of part A.

Answer 7

ok wait

Answer 8

I guess im confused they want a sentence how would i write that or am i reading into it to much :(

Answer 9

I can tell you what to write, but it's already written above.
Use your own calculation of the slope to show how you found the slope of f(x).
Then state that the slope of g(x) is 3 because g(x) is written in the slope-intercept form, which allows you to read the slope right off the equation.

Answer 10

oh ok sorry

Answer 11

so for part b f(x) is steeper/Bigger than G(x) because the slope of F(x) is 8 and the slope of G(x) is only 3 ... is this correct

Answer 12

@mathstudent55

Answer 13

Part A dealt with the slopes.
Part B deals with the y-intercepts, not slopes.

Answer 14

The y-intercept is the point where the line crosses the y-axis.
It is b in the slope-intercept equation of a line.

Answer 15

We know b for the g(x). It is -2 for g(x).
Now we need to find b for f(x).

Answer 16

Let's find the slope-intercept form of the equation of f(x)

y = mx + b

For f(x), we know m = 8 since we calculated it in part A.

We have:

y = 8x + b

Answer 17

We need to find b.
We can use any point in f(x) to find b.
Let's use point (0, -1)

y = 8x + b
-1 = 8(0) + b
-1 = b
b = -1

That means the equation of f(x) is:

f(x) = 8x - 1

Answer 18

Now we see the y-intercept of f(x) is -1, and the y-intercept of g(x) is -2.
Now we can compare them.

Answer 19

ohh so F(x) is bigger because it is -1 and G9x) is -2

Answer 20

that should say G(x) is -2

Answer 21

@mathstudent55

Answer 22

You are correct.

You mean to say:
The y-intercept of function f(x) is greater than the y-intercept of function g(x) because -1 is greater than -2.

Answer 23

awesome thank you

Answer 24

yw