Question 37555: If it costs $65 to travel 200km on a train and $80 to travel 350km, then;
a) express the cost, y, as a linear equation of distance traveled, x.
b) accordingly, how much would it cost to travel 500 km?
I have the answer which should be a) y= 0.010x + 45
b) $95
But have no idea how they got the answer. Should I be assigning two variables x and y to represent the unknow values. Write two equations using both variables and then solve the system of the given equations?
Not quite sure where to begin?
thank you
claudia
Answer by fractalier(6550)   (Show Source):
You can put this solution on YOUR website! If we let x be km traveled and y be the cost (in $), we have been given two points, (x, y). These points are (200, 65) and (350, 80). We treat these as any two (x, y) points. Let us first find the slope:
m = (y2 - y1) / (x2 - x1)
m = (80 - 65) / (350 - 200)
m = 15 / 150
m = 0.10
Now we use the point slope form to get the equation of the line:
y - y1 = m(x - x1) now plug in
y - 65 = .1(x - 200)
y - 65 = .1x - 20
y = .1x + 45
This IS the correct answer, not what you have. Notice the difference between .1 and .01
b) Now plug in x = 500
y = .1x + 45
y = .1(500) + 45
y = 50 + 45
y = 95
There you go...
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