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

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


   

Question 102072: Write the equation of the line L satisfying the given geometric conditions.
L has y-intercept (0,2) and is parallel to the line with equation 2x-3y=6

Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
Parallel lines have the same slope. Let's get the slope of the line you provided 2x-3y=6. The easiest way is to re-arranged the equation to the slope-intercept form, y=mx%2Bb where m is the slope and b is the intercept.
2x-3y=6
cross%282x%29-cross%282x%29-3y=6-2x Additive inverse of 2x
-3y=6-2x
cross%28-3%29%2Ay%2Fcross%28-3%29=%286-2x%29%2F%28-3%29
y=-2%2B2x%2F3
y=2x%2F3+-+2
+graph%28+300%2C+300%2C+-5%2C+5%2C+-5%2C+5%2C+2x%2F3-2%29+
The slope of your line is therefore m=2%2F3.
The line you're looking for is :
y+=+2x%2F3+%2B+b
with the point (0,2) you can calculate b.
2+=+2%280%29%2F3+%2B+b
b+=+2
Your final answer is
y+=+2x%2F3+%2B+2
+graph%28+300%2C+300%2C+-5%2C+5%2C+-5%2C+5%2C+2x%2F3-2%2C2x%2F3%2B2%29+