Question

module 11 (linear equations) assignment
score: 8/20 answered: 8/20
question 9
suppose you are in a submarine 55 feet below the surface of the water. you are ascending at a rate of 15 feet per minute. ( y = 15x - 55 ) models this situation. make a graph of this situation.
(graph grid shown)
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Explanation:

Step1: Identify the type of equation

The equation given is \( y = 15x - 55 \), which is a linear equation in the slope - intercept form \( y=mx + b \), where \( m = 15 \) (the slope) and \( b=- 55 \) (the y - intercept).

Step2: Find the y - intercept

To find the y - intercept, we set \( x = 0 \). Substituting \( x = 0 \) into the equation \( y=15x - 55 \), we get \( y=15(0)-55=- 55 \). So the y - intercept is the point \( (0,-55) \).

Step3: Find another point using the slope

The slope \( m = 15=\frac{15}{1} \), which means for every 1 unit we move to the right along the x - axis (increase \( x \) by 1), we move up 15 units along the y - axis (increase \( y \) by 15). Starting from the y - intercept \( (0,-55) \), if we increase \( x \) by 1 (let \( x = 1 \)), then \( y=15(1)-55=15 - 55=-40 \). So we have another point \( (1,-40) \).

Step4: Plot the points and draw the line

Plot the points \( (0,-55) \) and \( (1,-40) \) on the coordinate plane. Then, draw a straight line passing through these two points. Since the submarine is ascending, the domain of \( x \) (time in minutes) should be non - negative ( \( x\geq0 \) ) because time cannot be negative. Also, we can find when the submarine reaches the surface ( \( y = 0 \)) by solving \( 0=15x - 55 \).

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So the line should be drawn from \( x = 0 \) (when the submarine is at 55 feet below the surface) to \( x=\frac{11}{3}\) (when it reaches the surface) and beyond if we consider the submarine moving above the surface (though in the context of the problem, we can focus on the time when it is ascending from 55 feet below).

Answer:

To graph \( y = 15x-55 \):

1. Plot the y - intercept \( (0, - 55) \).
2. Plot the point \( (1,-40) \) (or any other point found using the slope).
3. Draw a straight line through these points, with \( x\geq0 \) (since time cannot be negative). The line represents the depth of the submarine (in feet below the surface, with negative values indicating below the surface and positive values indicating above the surface) as a function of time \( x \) (in minutes).