Question 1151480
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x = number of hours of tutoring
y = total cost


Smart student center learning, which I'll just abbreviate to "Company S", charges a registration fee of $25 plus an hourly rate of $30. This means the equation for Company S is 
y = 30x+25


Note how this equation is in the form y = mx+b
m = slope = 30
b = y intercept = 25
The slope tells us how much y goes up each time x increases by 1 (ie, for each increase of 1 hour, the cost goes up by $30)
The y intercept is the starting cost, or the cost if you have x = 0 hours of tutoring.


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I'll abbreviate "Brilliant learning center" as "Company B". This company has the following table of x,y values.
<table border = "1" cellpadding = "5">
<tr><td>x</td><td>y</td></tr>
<tr><td>1</td><td>45</td></tr>
<tr><td>3</td><td>115</td></tr>
<tr><td>5</td><td>185</td></tr>
<tr><td>7</td><td>255</td></tr>
</table>


Pick two points from that table, say the first two rows
Row1: (x1,y1) = (1, 45)
Row2: (x2,y2) = (3, 115)


Compute the slope between those two points
m = (y2-y1)/(x2-x1)
m = (115-45)/(2)
m = 70/2
m = 35
The slope is 35, which means Company B charges $35 an hour.


Use any row of the table as the (x,y) value. I'll use row 1, so (x,y) = (1,45)
Plug those values, along with m = 35, into the form
y = mx+b
and solve for b


y = mx+b
45 = 35*1+b
45 = 35+b
45-35 = b
10 = b
b = 10
The starting cost for Company B is $10, i.e. this is the registration cost or the cost of having x = 0 hours of tutoring.


Overall the equation for Company B is
y = 35x+10


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To summarize so far:

y = 30x+25 is the cost equation for Company S
y = 35x+10 is the cost equation for Company B


From here we plug x = 4 into each equation and simplify using PEMDAS


Company S
y = 30*x+25
y = 30*4+25
y = 120+25
y = 145
Having x = 4 hours of tutoring at Company S will cost you y = 145 dollars.


Company B
y = 35*x+10
y = 35*4+10
y = 140+10
y = 150
Having x = 4 hours of tutoring at Company B will cost you y = 150 dollars.


We see the difference of the two companies is 150-145 = 5 dollars. So Company S is cheaper by $5. Or put another way, Company B is $5 more expensive.


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Final Answer: 
<font color=red size=4>B) Brilliant student learning center charges $5 more than Smart student learning center.</font>
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