15. BRACELET A charm bracelet costs \( \$ 65 \), plus \( \$ 25 \) for each charm. The equation \( -25 x+y=65 \) represents the cost \( y \) of the bracelet, where \( x \) is the number of charms. a. Graph the equation. b. How much does the bracelet shown cost?

We are told that a charm bracelet costs a base price of US$65, and that each additional charm adds US$25 to the cost. (That is, Cost = 65 + 25×[number of charms].) The equation given is   –25x + y = 65. a. To graph this equation, first solve for y in terms of x:   –25x + y = 65 ⟹ y = 25x + 65. This is a linear equation with a slope of 25 and a y–intercept of 65. (The variable x represents the number of charms and y the total cost in dollars.) To graph the line on the coordinate plane: 1. Plot the y–intercept at (0, 65). 2. Use the slope. Since the slope is 25, for every 1 unit increase in x (one extra charm), y increases by 25 dollars. So when x = 1, y = 25(1) + 65 = 90. Plot the point (1, 90). 3. Similarly, when x = 2, y = 25(2) + 65 = 115. Plot (2, 115). 4. Draw the line through these points. Your graph should show a straight line starting at (0,65) and rising steeply with a rise of 25 dollars per extra charm. b. Part (b) asks, “How much does the bracelet shown cost?” In problems like this the picture would normally show the bracelet with a certain number of charms. For example, if the bracelet shows 3 charms (that is, if you count 3 charms on the image), then the cost would be computed by substituting x = 3 into the equation:   y = 25(3) + 65 = 75 + 65 = 140. Thus, if the bracelet has 3 charms, it costs US$140. (If the picture shows a different number of charms, substitute that number into y = 25x + 65 to find the cost.)