Question

part #7: use the graph below to answer each question
food supply
what does \x\ represent?
what does \y\ represent?
what is the y - intercept and what does it mean in terms of the food supply?
explain what the point (2, 62) means in terms of the food supply?
explain what the slope means for this situation.
how long until the food supply runs out?

Explanation:

Step1: Identify x - axis label

From the graph, the x - axis is labeled "Days". So, x represents the number of days.

Step2: Identify y - axis label

The y - axis is labeled "Lbs. of foods". So, y represents the amount (in pounds) of food supply.

Step3: Find y - intercept

The line intersects the y - axis at the point (0, 84). The y - intercept is 84. It means that at the start (day 0), there are 84 pounds of food supply.

Step4: Interpret the point (2, 62)

The point (2, 62) means that after 2 days, there are 62 pounds of food remaining in the supply.

Step5: Calculate slope

We use two points (0, 84) and (1, 73). The slope formula is $m=\frac{y_2 - y_1}{x_2 - x_1}$. So, $m=\frac{73 - 84}{1 - 0}=\frac{- 11}{1}=-11$. The slope of - 11 means that the food supply decreases by 11 pounds per day.

Step6: Find when food supply runs out

We know the equation of the line is $y=mx + b$ where $m=-11$ and $b = 84$. We set $y = 0$ and solve for $x$. So, $0=-11x+84$, then $11x=84$, and $x=\frac{84}{11}\approx7.64$. Since we are dealing with days, we can say it will take about 8 days for the food supply to run out.

Answer:

• x represents the number of days.
• y represents the amount (in pounds) of food supply.
• The y - intercept is 84. It means there are 84 pounds of food at the start.
• The point (2, 62) means there are 62 pounds of food after 2 days.
• The slope of - 11 means the food supply decreases by 11 pounds per day.
• It will take about 8 days for the food supply to run out.