Question 69068: Write the equation of the line L satisfying the given geometric conditions.
Please show how to work this out.
36. L has y-intercept (0,-3) and is parallel to the line with equation
y = 2/3 x -1.
40. L has y-intercept (0, 2) and is perpendicular to the line with equation
2x-3y -6.
Answer by jim_thompson5910(35256)   (Show Source):
You can put this solution on YOUR website! 36.
Any line that is parallel to a given equation, such as 2/3x-1, is going to have the same slope. So the unknown line's slope will be 2/3. Next since we have the y-intercept, we can use that to complete the unknown equation. In this case, problem 36 will have a slope of 2/3 and a y-intercept of (0,-3), so line L can be written as: y=2/3x-3.
40.
First we need to solve for y. Getting y to one side leaves you with: y=2/3x-2
To find a slope perpendicular to any given line, all you need to do is invert and negate (make the opposite sign) the given slope. In this case the given slope is 2/3, so the perpendicular slope is -3/2. All is left is to plug in the y-intercept to find the equation. So L should be: y= -3/2x+2
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