Question

Malia is observing the velocity of a cyclist at different times. After two hours, the velocity of the cyclist is 15 km/h. After five hours, the velocity of the cyclist is 12 km/h.
Part A: Write an equation in two variables in the standard form that can be used to describe the velocity of the cyclist at different times. Show your work and define the variables used. (5 points)
Part B: How can you graph the equations obtained in Part A for the first 12 hours? (5 points)

Answer 1

We must to remember what is the standard form of equation of straight line. It looks like that:
Ax+By+C=0.  A,B and C it's coefcients; x and y - it's variables.A and B must not be equal to zero at same time.This condition can be writen like this: (A^2+B^2) not equal to zero.
We know that x=2 ("after two hours") and y=15 ("velocity of the cyclist is 15 km/h")
AND
x=5 ("after five hours") and y=12 ("velocity of the cyclist is 12 km/h").
Lets look at standart form and give the values on variables.1. 2A+15B+C=0

2. 5A+12B+C=0and it is system.let's subtract the bottom equation from the top  -3A+3B=03A=3BA=B.So we can choose any value for A and B, just A=B.I choose for A=B=1.Our equation takes the formx+y+C=0
x+y=-C
and if we giving the value to variables, we can find coefficients "C".
5+12=-CC=-17.
Standart form is:x+y-17=0. ---- answer for Part A.
and the graph of this function is a straight line.For find the answer to Part B, we need to prolong our straight line into the perpendicular vertical line wich contain x=12.
In the point of the intersection of the lines, you must to turn at right angle to axis OY and to come at the value in the axis OY, it's will be the velocity after 12 hours.