Question

The art club is selling calendars to raise money to paint a mural. The cost of printing 3 calendars is $644.25, and for 5 calendars the cost is $653.75. Write an equation in slope-intercept form that represents the total cost, t, of printing the calendars, c.

Answer 1

To write the equation for the total cost (t) of printing c calendars, calculate the slope ($4.75 per calendar) from the given cost data for 3 and 5 calendars. Then, find the y-intercept (fixed cost) by substituting into the slope-intercept equation, yielding the final equation in the form t = 4.75c + b.

Step-by-step explanation:

To find the equation that represents the total cost, t, of printing c calendars, we need to determine the fixed cost and the variable cost per calendar. We are given two points: (3, $644.25) and (5, $653.75), which represent the number of calendars and the total cost, respectively.

First, we calculate the slope, which represents the variable cost per calendar, using the formula (change in cost)/(change in number of calendars), which is ($653.75 - $644.25)/(5 - 3). This gives us a slope of $4.75 per calendar. Next, we find the y-intercept by substituting one of the points into the equation t = mc + b, where m is the slope and b is the y-intercept. Using the point (3, $644.25), we get $644.25 = $4.75(3) + b. Solving for b gives us the fixed cost of printing calendars.

The slope-intercept form of the equation is t = 4.75c + b, where b is the y-intercept we just found.