00:01
In this problem, the first question is to determine the equation of the line passing through the point 1 negative 4 and perpendicular to the line 3x plus 2y minus 6 is equal to 0.
00:13
Now, if a line passes through the point x1 y1 and have a slop m, then the equation of the line can be determined as y minus y 1 is equal to m into x minus x1 which is the point.
00:30
Slop form.
00:32
Also if two lines are perpendicular to each other then if one line has slope m1 and the other line has slop m2 then the product of their slopes is negative one.
00:46
Also the slop intercept form of the equation of line is y is equal to mx plus c where m is the slop of the line and c is the y intercept.
01:03
Consider the line 3x plus 2y minus 6 is equal to 0.
01:08
Write it in the slop in recept form as 2y is equal to negative 3x plus 6 that is y is equal to negative 3 by 2x plus 6 by 2 which is 3.
01:22
This is a slop in recept form so that here we get the slop m of the line is negative 3 by 2 by comparing with the general form.
01:30
So that means if we name this as m1, then the slop m2 of the perpendicular line will be negative 1 divided by negative 3 by 2 since the product of the slops of the perpendicular lines will be negative 1.
01:46
Therefore the slop of the perpendicular line is 2 by 3.
01:50
Now we know that the perpendicular line passes through the point 1 negative 4 and it will have slop 2 by 3.
01:58
Therefore using this equation we can find the equation of the line.
02:02
Therefore the equation of the line is y minus y1 is negative 4 is equal to the slop m which is 2 by 3 times x minus x 1 x1 x1 here is 1.
02:14
Now simplification gives this as y plus 4 is equal to 2 by 3 x minus 2 by 3 that is we get y is equal to 2 by 3 x minus 2 by 3 minus 2 by 3 minus 2 by 3.
02:28
Is 4...