SOLUTION: HI! i need desperate help! please help me ! Any help will be Greatly appreciated!! graph the following information and see the q uestions below and answer them mass

Algebra ->  Linear-equations -> SOLUTION: HI! i need desperate help! please help me ! Any help will be Greatly appreciated!! graph the following information and see the q uestions below and answer them mass       Log On


   

Question 126330: HI!
i need desperate help!
please help me ! Any help will be Greatly appreciated!!



graph the following information and see the q uestions below and answer them
mass of loonies (g) , #of loonies
21 , 3
63 , 9
175 , 25
98 , 14
112 , 16

a) what is the mass of 33 loonies?
b) What is teh value of 133g of loonies?
c) A bag contains 152 g of coins. Is it possible that it contains only loonies? EXplain

Ps: the graph should be according with the questions I mean the values for teh x and y axis
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!



Finding the equation and graphing
Part A
Part B
Part C




Let x=mass of loonies (g) and y= # of loonies


When x=21, y=3. So we have the first point (21,3)


When x=63, y=9. So we have the second point (63,9)



So let's find the equation of the line through the points (21,3) and (63,9)


First lets find the slope through the points (21,3) and (63,9)

m=%28y%5B2%5D-y%5B1%5D%29%2F%28x%5B2%5D-x%5B1%5D%29 Start with the slope formula (note: is the first point (21,3) and is the second point (63,9))

m=%289-3%29%2F%2863-21%29 Plug in y%5B2%5D=9,y%5B1%5D=3,x%5B2%5D=63,x%5B1%5D=21 (these are the coordinates of given points)

m=+6%2F42 Subtract the terms in the numerator 9-3 to get 6. Subtract the terms in the denominator 63-21 to get 42


m=1%2F7 Reduce

So the slope is
m=1%2F7

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Now let's use the point-slope formula to find the equation of the line:



------Point-Slope Formula------
y-y%5B1%5D=m%28x-x%5B1%5D%29 where m is the slope, and is one of the given points

So lets use the Point-Slope Formula to find the equation of the line

y-3=%281%2F7%29%28x-21%29 Plug in m=1%2F7, x%5B1%5D=21, and y%5B1%5D=3 (these values are given)


y-3=%281%2F7%29x%2B%281%2F7%29%28-21%29 Distribute 1%2F7

y-3=%281%2F7%29x-3 Multiply 1%2F7 and -21 to get -21%2F7. Now reduce -21%2F7 to get -3

y=%281%2F7%29x-3%2B3 Add 3 to both sides to isolate y

y=%281%2F7%29x%2B0 Combine like terms -3 and 3 to get 0

y=%281%2F7%29x Remove the zero term




So the equation of the line which goes through the points (21,3) and (63,9) is: y=%281%2F7%29x

The equation is now in y=mx%2Bb form (which is slope-intercept form) where the slope is m=1%2F7 and the y-intercept is b=0

Notice if we graph the equation y=%281%2F7%29x and plot the points (21,3) and (63,9), we get this: (note: if you need help with graphing, check out this solver)

Graph of y=%281%2F7%29x through the points (21,3) and (63,9)

Notice how the two points lie on the line. This graphically verifies our answer.


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a)

"what is the mass of 33 loonies?"


To find the total mass (which is x) simply plug in y=33


y=%281%2F7%29x Start with the given equation

33=%281%2F7%29x Plug in y=33


33%2A7=x Multiply both sides by 7 to isolate x


231=x Multiply


x=231


So 33 loonies weigh 231 g

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b)

"What is teh value of 133g of loonies?"


First let's find the number of loonies (which is y)


y=%281%2F7%29x Start with the given equation


y=%281%2F7%29133 Plug in x=133


y=133%2F7 Multiply


y=19 Divide


So there are 19 loonies that weigh 133 g. So multiply the value of one loonie by 19 to find the total value.


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c)

y=%281%2F7%29x Start with the given equation


y=%281%2F7%29152 Plug x=152


y=152%2F7 Multiply


y=21.714 Divide


Since you cannot have 21.714 loonies, there must be other types of coins.