Notkcots college bookstore has been selling one particular sweatshirt for a year. During the fall semester, 260 were sold at a price of $24 each. During the following spring semester, the price was changed to $29. Consequently 210 were sold.
Suppose that the number of sweatshirts sold (N) depends linearly on the price charged (X). Write and equation showing this dependence.
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There are a few key words here, "linearly" and "depends." So we know the equation will be a line and that the dependent variable, X, will be the price charged.
You only need 2 points to draw a line, and we have those. When X=24, N=260. When X=29, N=210.
The form for a line is y-a=m(x-b). All we need now is the slope m, which is rise/run. or change in y over change in x. That's (210-260)/(29-24) or -10.
Now we have all our variables! Plug one of our points and the slope into the equation for a line: