Question

A committee has raised $230 in fundraising and continues toraise 30 dollars at each event they throw.-- Identify your independent and dependent variables- Write an equation to model the situationDetermine how much money will be raised after 10 events!Answer here:

Answer 1

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:

`(x_0,y_0)\text{ = ( 1,230 )}`

second event: 2, and the dollars raised is 230 + 30. That is, our second point is

`(x_1,y_1_{\text{ }})=(2,230+30)=(2,260)_{}`

Now, let's calculate the slope of the graph:

`m\text{ = }(y_1-y_0)/(x_1-x_0)=(260-230)/(2-1)_{}_{}_{}`

that is equivalent to say:

`m\text{ = }(260-230)/(2-1)\text{ = }(30)/(2)\text{ = 15}`

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.