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The highest rate on increasing is of 12x -6y = -24; Option B is the correct answer.
The options are given in the image attached with the answer
<h3>What is a Function ?</h3>A function is a law that relates a dependent variable and an independent variable.
It is asked among the options given , which is increasing at the highest rate.
To increase at a rate , the value of the slope , m should be > 0
For the Option 1
for a straight line function , the slope is given by
m = ( y₂ -y₁)/(x₂-x₁)
m = ( -3 -3)/(2- (-1)) = -6 /3 = -2
Therefore the function is decreasing
For Option 2
12x - 6y = -24
-6y = -12x -24
y = 2x +4
m = 2 (increasing)
For option 3
m = (-4 + 5)/(2-1) = 1
For Option 4
(8,0) (0,-4)
m = (-4 -0) /(0-8) = 4/8 = 1/2
The highest rate on increasing is of 12x -6y = -24
Therefore Option B is the correct answer.
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ANSWER
Length of the playing alley = 9m
Width of the playing alley = 3m
STEP-BY-STEP EXPLANATION:
Given information
<em>The perimeter of a rectangular playing alley = 24 m</em>
<em>The length of the alley is three times the width</em>
Let l represents the length of the alley
Let w represents the width of the alley
Step 1: Write the formula for calculating the perimeter of a rectangle
Where l is the length and w is the width of the rectangle
Recall, length = 3 times the width of the alley
Mathematically,
Step 2: Substitute the value of l = 3w into the above formula
Step 3: Solve for w
From the calculations above, you will see that the width of the playing alley is 3m
Step 4: Solve for l
Hence, the length of the playing alley is 9m