Question

The cost of providing water bottles at a high school football game is $25 for the

rental of the coolers and $0.65 per bottle of water. The school plans to sell water for $1.25 per bottle.
A. Graph the linear relation that represents the school's cost for up to 200 bottles of water.
B. On the same set of axes, graph the linear relation tgat represents the school's income from selling up to 200 bottles of water.
C. Write the equation representing each other.
D. What are the coordinates ofvthe point where the line cross?
E. What is the significance of this point?

Answer 1

A. To graph the linear relation representing the school's cost for up to 200 bottles of water, we can use the slope-intercept form of a linear equation: y = mx + b, where y is the cost, x is the number of bottles of water, m is the slope, and b is the y-intercept.

The y-intercept is the fixed cost of renting the coolers, which is $25. The slope represents the additional cost per bottle of water, which is $0.65. Therefore, the equation is:

y = 0.65x + 25

To graph the line, we can plot the y-intercept at (0, 25), and then use the slope to find additional points. For example, when x = 50, y = 0.65(50) + 25 = 57.50, so we can plot the point (50, 57.50) and draw a line through the points.

B. To graph the linear relation representing the school's income from selling up to 200 bottles of water, we can also use the slope-intercept form of a linear equation: y = mx + b, where y is the income, x is the number of bottles of water, m is the slope, and b is the y-intercept.

The y-intercept is the revenue from selling 0 bottles of water, which is $0. The slope represents the revenue per bottle of water, which is $1.25. Therefore, the equation is:

y = 1.25x + 0

To graph the line, we can plot the y-intercept at (0, 0), and then use the slope to find additional points. For example, when x = 50, y = 1.25(50) + 0 = 62.50, so we can plot the point (50, 62.50) and draw a line through the points.

C. The equation for the school's cost is y = 0.65x + 25, and the equation for the school's income is y = 1.25x + 0.

D. To find the coordinates of the point where the lines cross, we can set the two equations equal to each other and solve for x:

0.65x + 25 = 1.25x + 0

0.6x = 25

x = 41.67

Then we can plug in x = 41.67 into either equation to find y:

y = 0.65(41.67) + 25 = 52.08

Therefore, the point where the lines cross is (41.67, 52.08).

E. The significance of this point is that it represents the breakeven point, where the school's cost equals its revenue. If the school sells fewer than 41.67 bottles of water, it will not cover its costs. If it sells more than 41.67 bottles of water, it will make a profit.

Explanation: