how do you find the equation of this line; Slope=3 Y-Intercept=2 Using the Ax+By+C=0 method? and what does Ax, By and C suppose to mean? Thanks for any help!Please Register or Log in to view the hidden image!
If you're defining a line on a regular x-y plane, you can make the line equation a function of one variable (x or y). For slope=3, Y-Intercept=2, the basic equation (y=mx + b) is merely a reduction of your equation with the assumption that B=1. Thus Ax + By + C = 0 becomes -3x +y -2 = 0 and can be written as y = 3x + 2 . If B != 1, then you end up with y=(3x+2)/B. That's my educated guess.
It is for all I can see. If you want to define y in terms of x, then you substitute A for m and C for b s.t. y=(Ax + C)/B = (mx + b)/B The only thing about the generic y = mx + b equation that excludes the B term is an assumption that B is one or has already been divided into A & C.
Actually, there is an important difference between "Ax+ By+ C=0" form and "y= mx+ b". The second form cannot be used to represent a vertical line (x= 2 for example) while the first can. (It would be x-2= 0 with A= 1, B=0, C= -2.
qfrontier, You problem is to relate the undermined coefficients A, B and C to the slope and intercept. Let's look at the equation: Ax + By + C = 0 The y intercept is where x=0, so By<sub>intercept</sub> + C = 0 --- (1) The slope we get from rearranging the equation: By = -Ax - C y = -(A/B)x - (C/B) This is in the form y = mx + c, where m = -(A/B) and c = -(C/B) m is the slope, and c is the y intercept. Notice that if we rearrange equation (1) we get y<sub>intercept</sub> = -C/B, which agrees with this. You are given that Slope=3 Y-Intercept=2 so -C/B = 2 -A/B = 3 We have two equations and three variables, so we can set one of the variables arbitrarily. Let's choose B=1 for simplicity. Then: C = -2 and A = -3 The equation you want is: -3x + y - 2 = 0 or y = 3x + 2
