SOLUTION: Write the equation of the line L satisfying the given geometric conditions. L has Y-intercept (0,2) and is perpendicular to the line with equation 2x-3y=6 I am not sure exac

Algebra ->  Linear-equations -> SOLUTION: Write the equation of the line L satisfying the given geometric conditions. L has Y-intercept (0,2) and is perpendicular to the line with equation 2x-3y=6 I am not sure exac      Log On


   

Question 146253: Write the equation of the line L satisfying the given geometric conditions.
L has Y-intercept (0,2) and is perpendicular to the line with equation 2x-3y=6
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!

2x-3y=6 Start with the given equation.


y=%282%2F3%29x-2 Solve for y.


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


Now to find the slope of the perpendicular line, simply flip the slope m=2%2F3 to get m=3%2F2. Now change the sign to get m=-3%2F2. So the perpendicular slope is m=-3%2F2.


Now let's use the point slope formula to find the equation of the perpendicular 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-2=%28-3%2F2%29%28x-0%29 Plug in m=-3%2F2, x%5B1%5D=0, and y%5B1%5D=2


y-2=%28-3%2F2%29x%2B%28-3%2F2%29%28-0%29 Distribute


y-2=%28-3%2F2%29x%2B0 Multiply


y=%28-3%2F2%29x%2B0%2B2 Add 2 to both sides.


y=%28-3%2F2%29x%2B2 Combine like terms.


So the equation of the line perpendicular to 2x-3y=6 that goes through the point is y=%28-3%2F2%29x%2B2.


Here's a graph to visually verify our answer:
Graph of the original equation y=%282%2F3%29x-2 (red) and the perpendicular line y=%28-3%2F2%29x%2B2 (green) through the point .