The rate of change at which the water level rise is 13/6 cm/minute.The slope of the line is 13/6.The value of y is 23, (12,23).
Step-by-step explanation:
In the question the water rises 13 cm every 6minutes. Taking x to represent the time in minutes and y to represent the rise in cm then, find the rise y in time x as;
6 minutes=13 cm
1 minute=?---------------------perform cross multiplication
(1*13)/6=13/6
Hence in 1 minute, the rise is 13/6 cm
Thus in 12 minutes, the rise will be ;
12 * 13/6 = 2*13= 26 cm
(x,y) will be (12,26)
Finding the slope of the line using point (6,13) and (x,y)
[tex]m=\frac{y_2-y_1}{x_2-x_1} \\\\\\m=\frac{13-y}{6-x} \\\\\\m=\frac{13}{6} \\\\\\m=\frac{13}{6}[/tex]
The rate of change at which the water level rises equals the slope of the line.This is the justification.
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Answer:
The rate of change at which the water level rises is [tex]\frac{13}{6}[/tex]. So, solving the equation [tex]\frac{13}{6} =\frac{y-13}{12-6}[/tex] for y gives a y-value equal to 26.
Step-by-step explanation:
Here we can use the rule of three, if water level rises 13 centimetres every 6 minutes, after 12 minutes, how many centimetres will rise?
[tex]12 \ min \frac{13 \ cm}{6 \ min}=26 \ cm[/tex]
This means that after 12 minutes, the water level will be 26 centimetres height.
To show this as a slope, we use the definition:
[tex]m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]
We know that the two points are: [tex](6;13) \ (12;26)[/tex]
[tex]m=\frac{26-13}{12-6}=\frac{13}{6}[/tex]
This relation means that each 13 centimetres will be each 6 minutes. In other words, this is the rate of change.
