Question

suppose that you are driving to seattle at constant speed and noticed that after you have been travelling for 1 hours {i.e t=1},you have pass a sign saying it is 110 miles to saettle,and after driving another half hour you pass a sign saying it is 85 miles to seattle,using the horizontal axis for the time t and the vertical axis for the distance y from seattle,graph and find the equation y=mt+b for your distance from seattle find the slope, y-intercept and t-intercept and describe the practical meaning of each

Answer 1

Given :  driving to seattle at constant speed and noticed that after you have been travelling for 1 hours {i.e t=1},you have pass a sign saying it is 110 miles to saettle,and after driving another half hour you pass a sign saying it is 85 miles to seattle,

To find :   find the equation y=mt+b for your distance from seattle find the slope, y-intercept and t-intercept  

Solution:

y = mt + b

at t = 0

y  = b

=> b is the Distance of  seattle initially

at t = 1   Distance of  seattle = 110

=> 110 = m(1) + b

=> 110 = m + b

after driving another half hour you pass a sign saying it is 85 miles

=> t = 1.5     Distance of  seattle = 85

=> 85 = 1.5m  + b

=>   -15 = 0.5m

=> m = - 30

m = Speed  of 30 miles /hr

110 = -30 + b

=> b = 140

Distance of  seattle initially  = 140  miles

y = -30t + 140

at y = 0 => t = 140/30 = 14/3 hrs

m = Slope = - 30   =>  Speed   = 30 miles /hr

y intercept  =  140   => Distance of  seattle initially  =  140 miles

t intercept = 14/3   => Time taken to react seattle = 14/3 hrs = 4 hrs 40 mins

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Answer 2

Answer:

To find the slope m we have m=y2-y1/x2-x1

Put the values

m=(85-110)/(1.5-1)

m=-50

To find equation, we use point slope formula that is

y-y1/x-x1=m

Here this becomes

y-110/t-1=-50

This implies

Y=-50t+160 ... (A)

A is the required equation

Now for y intercept put t=0 in A

This implies y=160

It means the total distance was 160 miles

For t intercept put y=0 in A

Implies t=3.2

It means that total taken time to reach was 3.2 hours

Slope m=-50 means the speed for the unit hour

Minus sign shows that the distance was decreasing with further traveling