An on-line book club charges a membership fee and a constant rate for each book ordered.

Question

An on-line book club charges a membership fee and a constant rate for each book ordered. A membership and 4 books costs $52. A membership nad 7 books cost $76. This represents a linear function.

A. Find the rate of change (slope).

B. Write a Point-Slope equation.

C. Solve for Slope-Intercept form.

D. Solve for Standard form.

E. What is the SLOPE? What does the slope represent?

F. What is the y-intercept ? What does tit represent?

G. How much would a membership and 10 books cost?

Answer 1

A) Find slope: Assume $'s on y-axis and no. of books on x-axis. Slope = rise/run = (76 - 52)/(7 - 4) = 24/3 = 8.

So it looks like each book is $8.

B) Point-slope form would be y - 52 = 8(x - 4) using the first set of values, or (y - 76) = 8(x - 7) using the 2nd set. The general form is y - y₁ = m(x - x₁) where m is the slope. The first example uses point (52,4), the 2nd uses point (76,7).

C) Slope-intercept form: y = mx + b. b would be the y-intercept, where x = 0 (no books) and therefore would represent the membership fee. What's b? Try either of the two reference points. 52 = 8(4) + b,

b = 52 - 32 = $20 or 76 = 8(7) + b -> b = 76 - 56 = $20 (membership fee). S-I form is then y = 8x + 20 or T = 8B + 20, where T is total cost and B is no. of book purchased.

Could also find cost per book and membership fee by creating two simultaneous equations; M + 4B = 52 and M + 7B = 76. (M is membership fee, B = no. of books). The M's cancel, leaving 3B = 24, B = $8. The substitute M + 4(8) = 52 -> M = 52 - 32 = $20.

D) Standard form: Start with slope-intercept y = 8x + 20 and move the x term to the other side: y - 8x = 20

E) Slope is rise/run and represents the variable in this problem - the cost of a book.

F) Y-intercept - where the line crosses the x-axis (no book purchased) and thus represents the membership fee.

G) For a membership + 10 books use the slope-intercept form with B = 10.

Answer 2