Sam is observing the velocity of a car at different times. After three hours, the velocity of the car is 53 km/h. After six hours, the velocity of the car is 62 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?

Question

Sam is observing the velocity of a car at different times. After three hours, the velocity of the car is 53 km/h. After six hours, the velocity of the car is 62 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?

turingtest · Answer

ok, so I am guessing we can use point-slope formula

jolo_yolo · Answer

yeah. Im stuck now, idk what my next steps are since I've figured out the slope

turingtest · Answer

point-slope formula is$$y-y_1=m(x-x_1)$$so pick a point $(x_1,y_1)$ and plug it into the formula

jolo_yolo · Answer

okay so (3,53). Is it like 53 - 53(1) = 3(3 - 3(1)) ?

turingtest · Answer

no, you only plug in for $(x_1,y_1)$, you leave the regular $x$ and $y$ alone; we need them for the graph

jolo_yolo · Answer

oh k, 53 - y1 = 3(3-x1)

turingtest · Answer

you plugged into x and y, but you need to plug into $x_1$ and $y_1$

jolo_yolo · Answer

sorry i got that confused at first; y - 53 = 3(x - 3)

turingtest · Answer

good, now solve it for y

jolo_yolo · Answer

y=3(x-3) + 53; correct?

turingtest · Answer

yeah, but simplify the right side

jolo_yolo · Answer

y=3x + 44

turingtest · Answer

good, now what does x represent?

jolo_yolo · Answer

not sure, one of the points I think

turingtest · Answer

x is the left coordinate in our pairs
in the pair (3,53) what does the 3 represent?

jolo_yolo · Answer

hours?

turingtest · Answer

yes, and y represents...?

jolo_yolo · Answer

km or kilometers

turingtest · Answer

km/hr actually

turingtest · Answer

sorry i meant
let's say x=time and y=velocity

turingtest · Answer

|dw:1420068833152:dw|

turingtest · Answer

what is the speed of the car at time zero (i.e. at x=0) ?

jolo_yolo · Answer

uh idk, 0?

turingtest · Answer

no, use the formula we just developed
y=3x + 44

jolo_yolo · Answer

44?

jolo_yolo · Answer

@TuringTest

turingtest · Answer

ah yes, very good
let's mark that on the graph|dw:1420069303522:dw|what about at time equals one hour?

jolo_yolo · Answer

you mean as 1 for x?

turingtest · Answer

yep

jolo_yolo · Answer

47

turingtest · Answer

great, so let's mark that|dw:1420069483760:dw|are you seeing where this is going?

jolo_yolo · Answer

it's increasing by the hour? .-.

turingtest · Answer

sure, in the problem we see that it was going faster after 6 hours than after 3 hours, so it is accelerating

jolo_yolo · Answer

accelerating, right

turingtest · Answer

so just plug in the rest of the times and write down the corresponding speeds

jolo_yolo · Answer

oh okay so for part A my answer is y=3x + 44 and for par B i plug in 7 for x, right?

turingtest · Answer

well they want you to explain "how to graph it" so you need two points that you can draw a line though
so get the endpoints of x=0 and x=7 and draw a line through them

jolo_yolo · Answer

Alright, got it, Thanks ! much appreciated

turingtest · Answer

welcome!

chrisga · Answer

what was part B?