SOLUTION: Tutor could you please explain how to do this problem for me? Write the equation of the line L satisfying the given geometric condistions. 36. L has y-intercept (0,-3) an

Algebra ->  Linear-equations -> SOLUTION: Tutor could you please explain how to do this problem for me? Write the equation of the line L satisfying the given geometric condistions. 36. L has y-intercept (0,-3) an      Log On


   

Question 90411This question is from textbook Beginning Algebra
: Tutor could you please explain how to do this problem for me?
Write the equation of the line L satisfying the given geometric condistions.
36. L has y-intercept (0,-3) and is parallel to the line with equation y=2/3 x+1.
I have come up with y=2/3 x + -3 but I do not think this is correct. Any help you can provide with be great. Thanks. This question is from textbook Beginning Algebra

Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
Solved by pluggable solver: Finding the Equation of a Line Parallel or Perpendicular to a Given Line


Since any two parallel lines have the same slope we know the slope of the unknown line is 2%2F3 (its from the slope of y=%282%2F3%29%2Ax%2B1 which is also 2%2F3). Also since the unknown line goes through (0,-3), we can find the equation by plugging in this info into the point-slope formula

Point-Slope Formula:

y-y%5B1%5D=m%28x-x%5B1%5D%29 where m is the slope and (x%5B1%5D,y%5B1%5D) is the given point



y%2B3=%282%2F3%29%2A%28x-0%29 Plug in m=2%2F3, x%5B1%5D=0, and y%5B1%5D=-3



y%2B3=%282%2F3%29%2Ax-%282%2F3%29%280%29 Distribute 2%2F3



y%2B3=%282%2F3%29%2Ax-0%2F3 Multiply



y=%282%2F3%29%2Ax-0%2F3-3Subtract -3 from both sides to isolate y

y=%282%2F3%29%2Ax-0%2F3-9%2F3 Make into equivalent fractions with equal denominators



y=%282%2F3%29%2Ax-9%2F3 Combine the fractions



y=%282%2F3%29%2Ax-3 Reduce any fractions

So the equation of the line that is parallel to y=%282%2F3%29%2Ax%2B1 and goes through (0,-3) is y=%282%2F3%29%2Ax-3


So here are the graphs of the equations y=%282%2F3%29%2Ax%2B1 and y=%282%2F3%29%2Ax-3



graph of the given equation y=%282%2F3%29%2Ax%2B1 (red) and graph of the line y=%282%2F3%29%2Ax-3(green) that is parallel to the given graph and goes through (0,-3)





So you are correct