SOLUTION: Write an equation in slope-intercept form of a line with the following characteristics. Perpendicular to the graph of: y=3/2x-3 with a y-intercept of 5.

Algebra ->  Linear-equations -> SOLUTION: Write an equation in slope-intercept form of a line with the following characteristics. Perpendicular to the graph of: y=3/2x-3 with a y-intercept of 5.      Log On


   

Question 175879This question is from textbook
: Write an equation in slope-intercept form of a line with the following characteristics. Perpendicular to the graph of: y=3/2x-3 with a y-intercept of 5. This question is from textbook

Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
Note: a y-intercept of 5 means that the point (0,5) is on the graph.


We can see that the equation y=%283%2F2%29x-3 has a slope m=3%2F2 and a y-intercept b=-3.


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


Now let's use the point slope formula to find the equation of the perpendicular line by plugging in the slope m=3%2F2 and the coordinates of the given point .


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


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


y-5=%28-2%2F3%29x%2B%28-2%2F3%29%280%29 Distribute


y-5=%28-2%2F3%29x%2B0 Multiply


y=%28-2%2F3%29x%2B0%2B5 Add 5 to both sides.


y=%28-2%2F3%29x%2B5 Combine like terms.


So the equation of the line perpendicular to -3x%2B2y=-6 that goes through the point is y=%28-2%2F3%29x%2B5.


Here's a graph to visually verify our answer:
Graph of the original equation y=%283%2F2%29x-3 (red) and the perpendicular line y=%28-2%2F3%29x%2B5 (green) through the point .