SOLUTION: Write the equation of the line L satisfying the given geometric conditions: L has y-intercept (0,2) and is perpendicular to the line with equation 2x-3y=6 I have gone over and ov

Algebra ->  Linear-equations -> SOLUTION: Write the equation of the line L satisfying the given geometric conditions: L has y-intercept (0,2) and is perpendicular to the line with equation 2x-3y=6 I have gone over and ov      Log On


   

Question 65946: Write the equation of the line L satisfying the given geometric conditions:
L has y-intercept (0,2) and is perpendicular to the line with equation 2x-3y=6
I have gone over and over this and can not figure it out, and there is not an example that I can find in the book, which by the way is an online text so I do not have an ISBN number.
Answer by Earlsdon(6294) About Me  (Show Source):
You can put this solution on YOUR website!
Write the equation of the line whose y-intercept is (0, 2) and which is perpendicular to the line with equation: 2x-3y+=+6.
You can write the equation in the slope-intercept form. y = mx+b
You are given the y-intercept: b = 2
The slope can be found from the fact that it is perpendicular to 2x-3y = 6
Find the slope of the given line by rewriting it in the slope-intercept form.
2x-3y+=+6 Add 3y to both sides.
2x+=+3y%2B6 Subtract 6 from both sides.
2x-6+=+3y Divide both sides by 3.
%282%2F3%29x-2+=+y or
y+=+%282%2F3%29x-2 Compare this with:
y+=+mx%2Bb The slope of the given line is m = 2/3
A line that is perpendicular to this will have a slope that is the negative reciprocal of 2%2F3, so the slope of the new line is m+=+-3%2F2.
The equation of the new line is:
y+=-%283%2F2%29x%2B2