How do I solve this

Question

In 2002 PAC contributed $272 million to federal candidates. By 2008, the figure had risen to $ 402.8 million. Let A(t) represent the amount of PAC contributions, in million, and t the number of years since 2000. Find a linear function that fits the data.

 

I do not know what to do

 

Answer 1

Okay!

Your first step is to figure out what you already know from the problem.

1. The problem asks you for a linear function. That means a straight line. The basic function for a linear function is y=mx+b (this is the slope-intercept form, but that's going to be more useful to you than the standard form). Remember that m=the slope of the line and b=the y-intercept.

2. We know that t is the number of years since 2000, which means that in 2000 t=0 and in 2001 t=1. (t) is your x or independent value for this problem, so we can rewrite the formula above to y=mt+b.

3. We are given the values of the equation for two years. Those values are your y value.

4. From this information we have two points on the line. Using those, you can find the slope of the line. The slope of a line, remember, is made up of the difference in y divided by the difference in x. You can find these by subtracting the x values from each other (the difference of x) and the y values from each other (the difference in y). REMEMBER that the difference of Y goes in the numerator (on top) and the difference of x goes in the denominator (on bottom).
    a. Start with two points: (x₁, y₁) (x₂,y₂)
    b. Subtract the y values to find the difference of y: (y₂-y₁)

    c. Subtract the x values to find the difference of x: (x₂-x₁)

    d. Put the difference of y over the difference of x in a fraction and reduce, or divide to find a decimal depending on your teacher's instruction. y/x

 

5. Now we can plug this number into our original fraction in place of m.

6. Now all you need to do is find the y-intercept. You can do this by plugging one of the two points into the formula and solving for the missing variable. so:

    a. Plug one of your points into y=mt+b and make sure to include the slope.

    b. (b) should be the only variable in your equation now.

    c. Using standard rules for manipulating an equation, solve for b so b stands alone on one side of the equation. the number on the other side should be your y-intercept, or b.

 

7. Now this is VERY IMPORTANT. Double check your equation by plugging the t's from BOTH points into the equation and make sure you get the same answers, or y's, as were provided by the original question. If you do, then your equation is probably correct :). If you plug 0 in for t, you should get your y-intercept.

 

Hope that helped! Good luck!