Difference and limitations of point-slope, slope-intercept, intercept, two-point, general, parametric equations

Good LZ

Point-slope equation y-y1=k(x-x1), must satisfy that the slope exists, when the slope does not exist, this equation can not be listed

Slope-intercept equation y=kx+b, also must satisfy that the slope exists, when the slope does not exist, need to be discussed separately

Intercept equation x/a + y/b =1, this equation, in addition to the need to ensure that the slope exists, must also ensure that the slope k≠0, a≠0, general, parametric equation and limitations. In addition to the existence of slope, must also ensure that the slope k ≠ 0, a ≠ 0, b ≠ 0

Two-point equation (y-y1)/(y1-y2) = (x-x1)/(x1-x2), this equation also need to ensure that the existence of the slope and is not 0

Generic ax + by + c = 0 This equation can be applied to any straight line, there is no restriction, but the solution of the problem, if you bumped into the case of the line to find the general formula, you need to discuss separately. This equation can be applied to any straight line, there is no limitation, but if you hit a situation where you use the general equation to solve a straight line, 100% of the time it is a substitution for solving a system of quadratic equations, which is the most computationally intensive

Parametric equation for a straight line

x=x1+t

y=y1+kt

t is the number of directed segments formed by a point P on the straight line, and (x1,y1)

Generally, it can also be done

x=x1 +at

y=y1+bt (k=b/a)

Obviously, the restriction is also that k must exist