The minimum volume of the tank which is required for combined lengths of the fish is equal to 15-gallon tank.
What is a slope?
The slope of a line simply refers to the gradient of a line and it's typically used to describe both the ratio, direction and steepness of an equation of a straight line.
How to calculate the slope of a line?
Mathematically, the slope of a straight line can be calculated by using this formula;
[tex]Slope, m = \frac{Change\;in\;y\;axis}{Change\;in\;x\;axis}\\\\Slope, m = \frac{y_2\;-\;y_1}{x_2\;-\;x_1}[/tex]
By critically observing the graph of the capacity of the tank against the combined length of the fishes present in the tank, we can logically deduce that the y-intercept is 1, the point starts from (0, 1) and then passes through points (3, 4).
Substituting the given parameters into the slope formula, we have;
Slope, m = (4 - 1)/(3 - 0)
Slope, m = 3/3
Slope, m = 1.
Mathematically, the standard form of the equation of a straight line is given by;
y = mx + c
Where:
Also, we would find the total length of all the fishes in the tank:
Total length, x = (4 × 2) + (3 × 1) + (1 × 3)
Total length, x = 14 inches.
Next, we would write an expression for the equation of line of this graph:
y = 1(x) + 1
y = x + 1.
When x = 24, we have:
y = 14 + 1
y = 15-gallon tank.
In conclusion, the minimum volume of the tank which is required for combined lengths of the fish is equal to 15 inches.
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Complete Question:
You want to set up an aquarium and need to determine what size tank to buy. The graph shows tank sizes using a rule that relates the capacity of the tank to the combined lengths of the fish it can hold.
If you want four 2-inch platys, three 1-inch guppies, and a 3-inch loach, what is the smallest capacity tank you can buy?
17-gallon tank
13-gallon tank
15-gallon tank
14-gallon tank
