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Sagot :
Let's denote by x = the number of events.
and let's denote by y = the dollars raised.
Because the dollars raised to depend on the number of events, we can say that the dependent variable is y, and the independent variable is x. Now, we have the following data:
first event: 1, and the dollars raised is 230. That is, our first point is:
[tex](x_0,y_0)\text{ = ( 1,230 )}[/tex]second event: 2, and the dollars raised is 230 + 30. That is, our second point is
[tex](x_1,y_1_{\text{ }})=(2,230+30)=(2,260)_{}[/tex]Now, let's calculate the slope of the graph:
[tex]m\text{ = }\frac{y_1-y_0}{x_1-x_0}=\frac{260-230}{2-1}_{}_{}_{}[/tex]that is equivalent to say:
[tex]m\text{ = }\frac{260-230}{2-1}\text{ = }\frac{30}{2}\text{ = 15}[/tex]The equation for a line is y = mx + b. Now, let's calculate b
y = mx + b
so
b = y- mx
but m = 15, so the previous equation is equivalent:
b = y - 15x
if we choose the point (x,y) =(1,230) and we replace it in the previous equation we have:
b = 230- 15(1) = 230 - 15 = 215.
So, our equation of the line is :
y = 15x + 215
if x = 10 events we have :
y = 15(10) + 215 = 365 dollars
then, to the question: how much money will be raised after 10 events?, the answer is 365 dollars.
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