Question

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

Answer 1

so what is the equation ?

Answer 2

Part A: y intercept is at point (0,5) y intercept is 5
y intercept means when x = 0, y = a value

Answer 3

for any linear equation the slope intercept form is y = mx + b m is the slope of the line b is the y-intercept, or where the line cuts the y axis

Answer 4

Part B: Average rate of change =
\[\large \frac{ f(4)-f(1) }{ 4-1}\]

where f(4) means y value at x=4
where f(1) means y value at x=1
can you identify f(4) and f(1)? Tag me if you have questions.

Answer 5

how would i go about trying to find out f(4) and (f1)

Answer 6

Part C:
1. find slope.
\[ \large slope= \frac{ y_{2} - y_{1} }{ x_{2} - x_{1}}\]

y2= 27
y1= 5

x2= 1
x1=0

Can you plug these number in slope equation, and give me the slope?

Answer 7

Ok , Part B

what is y value at x=4?

Answer 8

Look on your chart.

Answer 9

the y value is 93 @study100

Answer 10

good, f(4) = 93
now can you find f(1) ?? = meaning y value at x=1

Answer 11

that would be 27 right @study100

Answer 12

Good, so using the equation
\[\frac{ f(4) - f(1) }{ 4-1 }\]
We have
\[\frac{ 93-27 }{ 3 }\]
= 22
This represent how much the displacement changes over the period of time from x=1 hour to x= 4 hours.
That's the answer for Part B.

Answer 13

Scroll back to my Part C. post, can you find slope? I have given you the values to plug in.

Answer 14

i found the slope to be 22 is that right? @study100

Answer 15

Good job :) it is!

Now using the slope intercept form

y= mx + b
y= 22x + 5 >>> (from what we know before, b, which is y intercept, is 5.)

Problem C tells us the turtle stops at y= 225 miles

225=22x+5

Solve for x. Lemme know if you have x

Answer 16

x=10?

Answer 17

Great job :)
The turtle starts at 0. Then it stops at 10

so your domain is from 0 hour to 10 hours.

\[0\le x \le 10\]

This is your answer for part C.

Answer 18

thank you so much!!!!!
i literally only have one more question like this and if you can i would so love your help!
@study100

Answer 19

I don't mind :)