Question

The table below represents a linear function f(x) and the equation represents a function g(x):


x
f(x)
-1
-11
0
-1
1
9
g(x)

g(x) = 5x + 1



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)

Answer 1

Can you make your table a little more organized, please? What exactly are the x points and which are their y's?

Answer 2

OK

Answer 3

Are the points (-1,-11), (0,-1), (1,9)?

Answer 4

YES

Answer 5

Ok, yeah those are the points. You just graph them to see that they are linear. To find the slope of the function using the points in your table, use the slope formula which is

Answer 6

still confused @IMStuck

Answer 7

It had to be RIGHT THEN that my computer chose to shut down and update. Sorry. Anyways, the slope formula is:

Answer 8

\[m=\frac{ y _{2}-y _{1} }{ x _{2}-x _{1} }\]using points from your table. Let's use points (0,-1) and (1,9) to find slope.

Answer 9

\[m=\frac{ 9-(-1) }{ 1-0 }=\frac{ 10 }{ 1 }=10\]The slope is 10 from the table. Got that?

Answer 10

The slope is 10 , got it

Answer 11

is that for part a

Answer 12

In g(x), the slope is given you in the way in which the equation is written. y = mx + b, where m is the slope. In your equation, y = 5x + 1, your slope is 5. And yes, what we did with the values from the table is for part a.

Answer 13

are we all done?

Answer 14

No, because we didn't do part b yet. We are done with part a.

Answer 15

ok i see now

Answer 16

For part b, we need to use the point-slope formula to find the equation and then the y-intercept. We need this formula for the point-slope:

Answer 17

\[y-y _{1}=m(x-x _{1})\]The value of y1 and x 1 come from a point that you choose from the table. Let's use the point (1,9) cuz it doesn't have any negatives in it. You fill in the x1 with 1, the y1 with 9, and the m with your slope of 10, like this:

Answer 18

ok

Answer 19

\[y-9=10(x-1)\]\[y-9=10x-10\]\[y=10x-1\]Now this is also in slope-intercept form
y = mx + b, where m is your slope (10) and b is your y intercept. Here, the -1 is in the b position, so your y intercept for this equation is -1. In g(x) = 5x+1, the +1 is in the b position, so your y intercept for g(x) is +1.

Answer 20

g(x) has a greater y intercept because it is positive 1 and the y intercept from your table is -1.

Answer 21

thanks for ur help , i get it now

Answer 22

Good! Glad to help!