Test 4 Section 4 Number 17. Could you give me the explanation for this problem? Thank you!
Sure! For questions like this, it’s really helpful to remember that the slope of any line represents the line’s rate of change—it represents how much the y-variable changes when the x variable changes. Applied to this question, the slope tells you how much the total cost of buying materials and renting tools (the y-variable) changes when the number of days (the x-variable) changes.
Because the materials cost is constant, only the tool rental costs change from day to day. Therefore, the slope tells you the daily rental cost of the tools.
You can also see this algebraically if that conceptual explanation falls flat. The question tells you that the equation for total cost y in terms of days x is:
y = M + (W + K)x
At Store C, which is the store question 17 is concerned with, we know from the table that M = 700, W = 20, and K = 70. Therefore:
y = 700 + (20 + 70)x
y = 90x + 700
That’s the standard slope-intercept form of a line, y = mx + b, where m is the slope and b is the y-intercept. So the slope of the line will be 90, which is the total daily rental cost of the wheelbarrow and cement mixer.