Glen is sinking in quicksand. He sinks 1 inch every 4 seconds. Make an equation and graph the equation

Answer 1

Anytime you are provided a word problem you must first identify your variables. Usually the best way is to figure out what units you are working with. In this case it is inches and seconds. Because we are measuring distance over time we should assign inches to the y-axis and seconds to the x-axis. With this in mind we have to make an equation. This equation should be linear because we are told that Glen is sinking at a constant rate. Now we must write an equation in the form of y=ax+b.

In order to derive this equation we must figure out what is the coefficient (a) and the constant (b) are. We can find the coefficient (also known as slope) with the information provided in the question. The slope is (change in y)/(change in x). So for every 1 inch in the y axis we go 4 seconds on the x axis. So we divide 1 by 4 to get 1/4. But remember Glen is sinking so he is going down the y axis so the slope should be negative. As a result the slope is -1/4. We now have y= -1/4x+c, so what is the constant (b)? We aren’t provided any information about the height where Glen started at so we can assume he was at ground level. This makes b=0 and as a result our is equation is y=-1/4x.

To plot this you would start at the point (0,0) then substitute x=1, x=2, and so on into the equation (y=-1/4x) and solve for y each time. Once you get enough points you can draw a straight line. In this case you should draw a line to the right of the y axis because we can’t go back in time so x should never be a negative number.

Use this thought process to solve more world problems like this and you will always succeed. Please message me if you need anymore help!