SOLUTION: The equation of the line L is 3y - x=9. Find a) The coordinates of the point where l intersects the y- axis. b) The equation of the line which is parallel to l and which passes

Algebra ->  Test -> SOLUTION: The equation of the line L is 3y - x=9. Find a) The coordinates of the point where l intersects the y- axis. b) The equation of the line which is parallel to l and which passes       Log On


   

Question 205699: The equation of the line L is 3y - x=9. Find
a) The coordinates of the point where l intersects the y- axis.
b) The equation of the line which is parallel to l and which passes through the point (0, -5)
Answer by tutor_paul(519) About Me  (Show Source):
You can put this solution on YOUR website!
3y-x=9
The point where a line crosses the Y-axis is called the "Y-Intercept." The easiest way to determine the Y intercept when you are given the equation of the line is to write the equation in y=mx+b form. the "b" term is then just read off the equation as the Y-intercept.
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3y-x=9
3y=x%2B9
y=x%2F3%2B3
So now that you have the equation written in the proper form, you can easily see that the Y-intercept=3.
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To do the 2nd part of the problem, you need to know that 2 lines are parallel if they have the same slope. When the equation of a line is written in y=mx+b form, the slope is just the "m" term. In our case, the slope is 1/3. You are also given the fact that the line passes through the point (0,-5). Since the x term of this coordinate is zero, you know that the Y-intercept is just the Y-coordinate, which is -5. So now that you have the slope and the Y-intercept, it is a simple matter to write the equation of this second line:
highlight%28y=x%2F3-5%29
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Good Luck,
tutor_paul@yahoo.com