SOLUTION: Find the equation of the line perpendicular to the line y = 2x - 3 which contains the point (1,3). Express answer in slope-intercept form.

Algebra ->  Linear-equations -> SOLUTION: Find the equation of the line perpendicular to the line y = 2x - 3 which contains the point (1,3). Express answer in slope-intercept form.      Log On


   

Question 323861: Find the equation of the line perpendicular to the line y = 2x - 3 which contains the point (1,3). Express answer in slope-intercept form.
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

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


Now to find the slope of the perpendicular line, simply flip the slope m=2 to get m=1%2F2. Now change the sign to get m=-1%2F2. So the perpendicular slope is m=-1%2F2.


Now let's use the point slope formula to find the equation of the perpendicular line by plugging in the slope m=-1%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-3=%28-1%2F2%29%28x-1%29 Plug in m=-1%2F2, x%5B1%5D=1, and y%5B1%5D=3


y-3=%28-1%2F2%29x%2B%28-1%2F2%29%28-1%29 Distribute


y-3=%28-1%2F2%29x%2B1%2F2 Multiply


y=%28-1%2F2%29x%2B1%2F2%2B3 Add 3 to both sides.


y=%28-1%2F2%29x%2B7%2F2 Combine like terms. note: If you need help with fractions, check out this solver.


So the equation of the line perpendicular to y=2x-3 that goes through the point is y=%28-1%2F2%29x%2B7%2F2.


Here's a graph to visually verify our answer:


Graph of the original equation y=2x-3 (red) and the perpendicular line y=%28-1%2F2%29x%2B7%2F2 (green) through the point .