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

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


   

Question 57071: L has y-intercept (0, 2) and is perpendicular to the line with equation 2x - 3y = 6.
Write the equation of the line L satisfying the given geometric conditions.
Answer by funmath(2933) About Me  (Show Source):
You can put this solution on YOUR website!
L has y-intercept (0, 2) and is perpendicular to the line with equation 2x - 3y = 6.
Write the equation of the line L satisfying the given geometric conditions.
:
First we need to find the slope of the line that they gave you. When you need to find the slope of a linear equation, put the equation in slope-intercept form: highlight%28y=mx%2Bb%29, where m=slope and (0,b)=y-intercept.
2x-3y=6
-2x%2B2x-3y=-2x%2B6
-3y=-2x%2B6
-3y%2F-3=%28-2%2F-3%29x%2B6%2F-3
y=highlight%28%282%2F3%29%29x-2, the slope of this line is:m=2/3
:
Perpendicular lines have slopes that are negative reciprocals of each other, so change the sign and flip the slope upside down.
The slope of the line we are writing an equation of is: m=-3/2 and the y-intercept is (0,b)=(0,2) Plug these values into the slope intercept form of a line:
y=highlight%28%28-3%2F2%29%29x%2Bhighlight%282%29
highlight%28y=%28-3%2F2%29x%2B2%29
Happy Calculating!!!