Amanda V. answered • 10/15/21
Passionate High School Math Teacher
The best way to solve this is to start with putting the line into slope-intercept form (y=mx+b) where m is the slope and b is the y-intercept.
So to start you would need to isolate the y. To do so subtract 3x from both sides of the equation.
3x+3y=45
-3x. -3x
3y=-3x+45
Then you'll need to divide every term by the coefficient of y (which is 3 in this case
3y=-3x+45
/3 /3 /3
y=-x+15
Now you have your slope.. the slope is -1. In order to find a line perpendicular to this line you will need to find the opposite reciprocal of -1 (flip the fraction and flip neg to pos). so the slope of the perpendicular line should be 1.
Amanda V.
While that makes sense and is true. I should have said easiest instead of best. I found that if a high schooler is first learning this concept, converting to slope-intercept form is easiest. This is indeed more efficient, but my students find that concept really hard to grasp.10/16/21
David W.
Agreed ... "first learning" should be like 'training wheels" on a bicycle. Once Ax+By=C is converted to slope-intercept form, students (who are always on the lookout for 'easy') will realize that (-A/B) is PRETTY EASY. AND,10/16/21
David W.
... when faced with standardized tests with limited time, they will benefit.10/16/21
Amanda V.
Oh for sure10/16/21
David W.
Don't forever convert to slope-intercept form. The slope of Ax+By=C is (-A/B). All perpendicular lines have a slope of (B/A). Here, that is (3/3) = 1.10/16/21