a We have been told that the crew is beginning their journey with 145 pounds of food. Also, the crew eats 15 pounds of food per day. We will write the equation of the situation in slope-intercept form.
y=mx+bIn this equation m is the slope and b is the y-intercept. If x represents the number of days that have passed, then 15x gives the amount of food that is eaten.
The total amount of food: 145
The eaten amount of food: 15x
Subtracting the eaten amount from the total amount of food will give y, the remaining food.
y= 145- 15x
⇓
y=- 15x +145
Notice that the slope is negative because the amount of food decreases per day.
b We need two points to draw a graph. Therefore, we will plot the y-intercept and use the slope to find a second point.
Let's connect these two points to draw a line. Note that our function has a maximum at x=0 because there cannot be a negative number of days. We also have a minimum at y=0 because we cannot have a negative amount of food.
c We want the remaining food to be 25 pounds when they end their voyage. Since y represents the remaining food, we can substitute 25 for y into the function to find the number of days the voyage will last.
