SOLUTION: Write the equation of the line L satisfying the given geometric conditions. L has Y-intercept (0,-3) and is parallel to the line with equation y=2/3x+1 - did not match any docu

Algebra ->  Numeric Fractions Calculators, Lesson and Practice -> SOLUTION: Write the equation of the line L satisfying the given geometric conditions. L has Y-intercept (0,-3) and is parallel to the line with equation y=2/3x+1 - did not match any docu      Log On


   

Question 146252: Write the equation of the line L satisfying the given geometric conditions.
L has Y-intercept (0,-3) and is parallel to the line with equation y=2/3x+1 - did not match any documents.
I am not sure exactly what they are asking for can you please help me with this.
thanks
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

We can see that the equation y=%282%2F3%29x%2B1 has a slope m=2%2F3 and a y-intercept b=1.


Since parallel lines have equal slopes, this means that we know that the slope of the unknown parallel line is m=2%2F3.
Now let's use the point slope formula to find the equation of the parallel line by plugging in the slope m=2%2F3 and the coordinates of the given point .


y-y%5B1%5D=m%28x-x%5B1%5D%29 Start with the point slope formula


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


y%2B3=%282%2F3%29%28x-0%29 Rewrite y--3 as y%2B3


y%2B3=%282%2F3%29x%2B%282%2F3%29%28-0%29 Distribute


y%2B3=%282%2F3%29x%2B0 Multiply


y=%282%2F3%29x%2B0-3 Subtract 3 from both sides.


y=%282%2F3%29x-3 Combine like terms.


So the equation of the line parallel to y=%282%2F3%29x%2B1 that goes through the point is y=%282%2F3%29x-3.


Here's a graph to visually verify our answer:
Graph of the original equation y=%282%2F3%29x%2B1 (red) and the parallel line y=%282%2F3%29x-3 (green) through the point .