b) The water line is given by the equation y=-2/3x-12. Suppose you want to put a pink flamingo lawn ornament in your backyard, but you want to avoid placing it directly over the water line, in case you need to excavate the line for repairs in the future. Could you place it at the point (-4,-10)?
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y=4x
To answer this question, we need to determine whether the point (-4,-10) lies on the water line given by the equation y = -2/3x - 12.
To check if the point satisfies the equation, we substitute the x and y values of the point (-4,-10) into the equation:
y = -2/3x - 12
Replacing x with -4 and y with -10:
-10 = -2/3(-4) - 12
Simplifying further:
-10 = 8/3 - 12
-10 = 8/3 - 36/3
-10 = -28/3
Since -10 is not equal to -28/3, the point (-4,-10) does not lie on the water line given by the equation y = -2/3x - 12.
Therefore, you can place the pink flamingo lawn ornament at the point (-4,-10) without it being directly over the water line.