Algebra1 formula, what does y2 - y1 over x2 - x1 mean?

This appears to be about plotting positions on a graph;

x1=0

y1=2

x2=1

y2=4

which should mean that each increase in x is by 1, and of y by 2

and m would be (4-2)/(1-0) which is 2/1 or 2.

That formula is to find the slope of a line. If the line is very steep, the slope is large. If the line is not so steep the slope is a smaller number. If the line rises on the page from left to right, the slope is positive and if it falls on the page, the slope is negative. Vertical lines have no slope and horizontal lines have a slope of zero. For some reason the letter "m" stands for the word "slope" In your example, for the point (0,2) the y number is "2" and for the point (1,4) the y number is "4". On the top (numerator) of the fraction you would have "2-4" or "-2". To get the bottom(denominator) of the fraction you use the "x" numbers. So for the point (0,2) the x number is 0 and for the point (1,4) the x number is 1. So subtract "0-1" and you get " -1". Now when you put "-2" on the top (from the y answer) and "-1" on the bottom (from the x answer) your answer is "-2" over "-1" which when reduced becomes positive 2. So your line has a fairly steep slope and rises up to the right on your graph. If you practice this formula with different pairs of points, you will see why vertical lines have no slope. You get a zero on the bottom of the fraction and since you can never divide by zero, they do not have a slope. For horizontal lines, the slope formula gives a zero on the top and that is okay and gives an answer of zero. Slope is a very useful concept in the building trades. One word of caution is to be consistent on the order of your subtraction. When you start with one point for subtracting the "y" numbers, you must start with that same point for subtracting the "x" numbers. Hope this helps and is not too confusing. Good luck in your math endeavors.

It is the equation for the slope of a line. If the answer is zero, then there is no slope and the line is completely horizontal, looks like this: _________

The example you gave would be 4-2 over 1-0 which is 2 over 1 or 2/1. Which means that your line will have values starting from your y-intercept and going up 2 numbers and 1 to the right, and down 2 numbers and 1 to the left.

Sorry if I confused you!

This formula is used to determine the slope of a line. The slope of a line (which is commonly called m) is the rise of the line (x2-x1) over the run of that same line (y2-y1). You can use this formula to find other coordinates on the same line if you have a single point and the slope or 2 points, then you can figure out the slope using this formula to find other unknown coordinates

this formula is used to find the gradient

so 4 - 2 / 1 - 0 >>>> 2 / 1 = 2

it is subtracted for multiplied