Question

PLEASE HELP!!!!!!

Sam is observing the velocity of a car at different times. After two hours, the velocity of the car is 50 km/h. After six hours, the velocity of the car is 54 km/h.

Part A: Write an equation in two variables in the standard form that can be used to describe the velocity of the car at different times. Show your work and define the variables used.

Part B: How can you graph the equation obtained in Part A for the first seven hours?

Answer 1

@nikato @jim_thompson5910 @mathslover

Answer 2

are you able to get started?

Answer 3

ya

Answer 4

what do you have so far

Answer 5

i don't know what to do

Answer 6

but you said you were able to get started?

Answer 7

i thought you meant was i able 2 get started on the problem with u

Answer 8

ok let's start off defining the variables

Answer 9

what are the two variables?

Answer 10

idk

Answer 11

read the problem again and think it over

what two things are we trying to connect?

Answer 12

the velocity of 2 and 6 hours?

Answer 13

velocity is one variable

what's the other?

Answer 14

the car?

Answer 15

no, what's another thing that has some numerical values to it

Answer 16

the time?

Answer 17

good, the two variables are time and speed (velocity)

Answer 18

ok

Answer 19

so let's define

x = time
y = speed

Answer 20

"After two hours, the velocity of the car is 50 km/h"

that means

x = 2
y = 50

Answer 21

giving us the point (2,50)

Answer 22

what's the other point?

Answer 23

(6,54)?

Answer 24

now find the slope of the line through the two points (2,50) and (6,54)

Answer 25

how do i do that?

Answer 26

using the slope formula

m = (y2 - y1)/(x2 - x1)

Answer 27

basically, you subtract the y coordinates
then subtract the x coordinates (same order)
finally, divide to get the slope (y over x)

Answer 28

I got 1

Answer 29

me too

Answer 30

so m = 1

Answer 31

Now plug m = 1, x = 2 and y = 50 into y = mx + b and solve for b

y = mx + b

y = 1*x + b

50 = 1*2 + b

...
...
...

b = ???

Answer 32

48?

Answer 33

good

Answer 34

so the equation is

y = 1x + 48

or just

y = x + 48

Answer 35

notice how when x = 2, y is...

y = x + 48

y = 2 + 48

y = 50

so when the time is 2 hrs, the speed is 50 km/hr

Answer 36

also, notice how when x = 6, y is...

y = x + 48

y = 6 + 48

y = 54

so when the time is 6 hrs, the speed is 54 km/hr

Answer 37

ok, but how do i put that in standard form like the question asks?

Answer 38

now you must convert y = x + 48 into the form Ax + By = C

Answer 39

how?

Answer 40

by getting that x over to the left side

Answer 41

can u show me how 2 do that?

Answer 42

think of x+48 as 48+x

Answer 43

y = 48+x

how do we move that +x over?

how do we get rid of it on that right side?

Answer 44

by subtracting it?

Answer 45

good