Question

How do graphs and equations reveal information about a relationship between two quantities

Answer 1

Let the quantities be x and y.

Graphs tell exactly (or at least approximately) the value/s of x for a certain known y, 

or the opposite, assume we want to find y for x=2.5.

We check the graph on the point with x=2.5, and we can see what y is.

check the picture of the graph of y=-3x-xe^2x, generated by desmos.com

assume we want to know what is the value of x for which y=5.

if we click on the point with y-coordinate =5, we see that x=-1.67.

But even without doing this, we can tell that x is a value between x=-2 and x=-1, almost in the middle, but a little more near x=-2.

So we could give an approximation of -1.6 or -1.7, which may be good enough.




An equation also tells what y is, for a given x, or the other way around.

Sometime substituting x with a known value may give an expression in terms of y which is hard to solve,  

but for that particular x, the expression in terms of y is uniques, even if a certain value is not produced.

Consider again the equation y=-3x-xe^2x, 

for x=2, we can tell that y=-6-2e^4


for y=8, we can say that 

8=-3x-xe^2x, and really not be able to solve it, but we can approximate x by checking some values, which is still better that having no clue at all.