First, here's a note about notation. When typing algebraic ratios, we must enclose numerators and/or denominators in grouping symbols, if they contain more than one term. Without those added parentheses, your typing means this instead (due to Order of Operations rules):
\(\displaystyle y1 - \dfrac{y2}{x1} - x2\)
You titled your post, "When trying to find [the] y-intercept", but the ratio (y1-y2)/(x1-x2) gives you the slope of the line, not the point where the line crosses the y-axis.
Depending on what information you were given about the line, you may not need to calculate the slope, if what you're looking for is the y-intercept. Please provide the entire exercise statement, so that we can see everything that you were given.
You asked why the Slope Formula has the difference of the y-coordinates in the numerator and the difference of the x-coordinates in the denominator, instead of the other way around. The short answer is because slope is defined that way; slope is the ratio "change in y" to "change in x" (going from one point on the line to another). :cool:
sorry for my confusion I thought y intercept, because i thought you had to find slope first in order to find our b and that b in y=mx+b was our y intercept. Thanks for your help, i just noticed it seemed to get me the same answer when I did (y1-y2)/(x1-x2) or switched it to (x1-x2)/(y1-y2)