Which system of equations is represented by this table of values?

can you explain as well but like you don't have to but try.

  see below

Step-by-step explanation:

As is often the case with multiple choice questions involving linear equations, a suitable solution strategy is to eliminate the choices that don't make any sense.

Here, you're given all of the answer choices in slope-intercept form. You are also given a line for x=0 in the table, so the table values on that line give the intercepts of the functions.

f1 has a "y-intercept" of -2, eliminating the upper right and lower left answer choices.

When x increases by 1, from 0 to 1, f1(x) increases by 2, from -2 to 0. So, the coefficient of x in the equation for f1(x) will be 2, matching the upper left answer choice.

You can try other table values in those equations to check that they work. It is usually sufficient to check one other value (since you already know the equations work for x=0). x=1 is often a convenient value to use.

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In slope-intercept form, the equation for a line is ...

  y = mx + b

where m is the slope and b is the intercept. The intercept is the value of y when x=0.

The slope is the amount of increase of y when x increases by 1.

take the logarithm of both sides (the base of the log doesn't matter):

apply the exponent property - this says that :

distribute the log terms on both sides:

group like terms together:

divide through both sides by the coefficient on :

you can do some additional rewriting here using the properties of the logarithm to simplify things if you like: