Algebra 2 (1st Edition)

$y=4x+11$
The first step is to check how the numbers are progressing. Do the values progress through addition, subtraction, multiplication, or division? The equation is going to be in the format $y=mx+b$, and since the first $x$-value of $0$ corresponds to a $y$-value of $11$, if you substitute in the known values of $y$, $x$, and $b$, we would get $11=0m+b$. Because of the Zero Product Property, the product of $0$ and any other number is $0$, so the above equation results in $b=11$. Therefore, we can amend the general formula for the equation ($y=mx+b$, as mentioned above) to say $y=mx+11$. Now we can use another pair of $x$ and $y$ values to find the value of $m$. If we use the second pair, $15=1m+11$ $1m=m$, so $15=m+11$ $m=4$. Plugging in the known values of $m$ and $b$, the equation to represent this table is $y=4x+11$. It's probably a good idea to see if this equation applies to other $x$-and-$y$-value pairs, just to make sure. The third pair, for example, is 2 and 19. $19=(4\times2)+11=8+11=19$ $19=19$ Because the above statement works out to be true, the equation $y=4x+11$ does, in fact, apply to this question.