Standard Form is another way to write the equation of a line. The Standard Form equation is Ax+By=C. A, B, and C all represent coefficients. It's similar to Slope-Intercept Form, however, x and y are on the same side, unlike the prior. The slope in Standard Form is represented by the "A" and the "C" represents the y-intercept. To turn Standard Form into Slope-Intercept Form, you add or subtract (depending on whether A is positive or negative) the "Ax" to the other side, so you get By=-Ax+C. Then, you divide "Ax+C" by B, and you get your equation into Slope-Intercept Form. To turn Slope-Intercept into Standard Form, you add or subtract (depending if m is positive or negative) the "mx" to the other side so that you get "Ax+By=C." Another helpful tip to remember when learning Standard Form is that "A" should NOT be negative. Try this practice problem below!
Try finding this in Slope-Intercept Form, and transfer it into Standard Form!
First, find the Slope-Intercept Form equation of the line. Remember, to find the slope, do y2-y1/x2-x1. When you do this, you should get 2-5/-1-2, which equals a slope of -3/-3, or 1. Then, you need to find the y-intercept. This is the point where the line hits the y-axis. On this problem, that point is at (0,3). Now, you have a Slope-Intercept equation of y=1x+3. Then, follow the steps that I talked about above to transfer this equation into Standard Form. This is pretty easy to remember, because you just need to subtract 1x from each side. You know have an equation of -1x+y=3. Also, since A cannot be negative, you need to divide the whole equation then by -1 (just for this case) so that your A value can be positive. After doing this, you have your Standard Form equation of 1x-y=-3.