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# 4. Using the line equation

## Video transcript

there's a detail that we need to attend to there's a slight problem with the slope-intercept form of the scene geometry the problem is that if a B is vertical the slope isn't defined to see that look at the slope-intercept form in general y equals MX plus I where m is the slope and I is the y-intercept the slope M is the change in Y divided by the change in X meaning that if a B is a vertical line there is no change in X so computing the slope would mean dividing by zero which is bad but we can eliminate this problem by multiplying through by the change in X so multiplying through by the change in X we get change in x times y equals change in Y times X plus I times change in X it's common to move everything to one side and rewrite this as change in Y times X minus change in x times y plus I times change of x equals zero call this term change in Y a value a this term negative change in X a value B and this term I times change of X a value C meaning we can write an equation for the line as ax plus B y plus C equals zero an equation like this for a line goes by several names it's sometimes called the line equation it's also called the implicit form for the line let's do an example for this specific line a B change in Y is negative 3 change in X is 1 and I is 11 so negative 3x minus y plus 11 equals 0 that line equation is shown here notice that as I move a and B around the line equation updates accordingly the line equation can be used with the parametric form of the Ray to compute intersection points this time for any type of line even vertical ones use the next exercise to practice computing intersection points using line equations