Question

Gregory has agreed to donate $250 to Spring Valley High School for its library. In addition, he will donate $5 for every book a student at Spring Valley School reads during the summer. The sequence shown represents the possible amounts that Gregory will be donating for the summer. 250, 255, 260, 265, 270, 275, … Write the above sequence as a function in the form f(x) = mx + b

Answer 1

f(x) = 5x + 250 As given in the problem, you need to make a function of the form f(x) = mx + b. So first, determine the value of m by taking the difference in y over the difference in x for two points on the desired line. You know that if 0 books are read, Gregory will be donating $250. So one point is (0,250). And if 1 book is read, Gregory will be donating $255. So another point is (1,255). So the slope is the difference in y (255-250 = 5) dividing by the difference in x (1 - 0 = 1), so 5/1 = 5, therefore the function now looks like f(x) = 5x + b Now we need to determine b is. For that, just substitute any known pair of x and y values and solve for b. Since we already used (0,250) above, we'll use them again. So substitute into the equation. f(x) = 5x + b 250 = 5 * 0 + b 250 = 0 + b 250 = b So the completed function is f(x) = 5x + 250