SOLUTION: Find the x-intercept of the straight line passing through P = (2, 3) and perpendicular to y + 3x = 8 .

Algebra ->  Coordinate-system -> SOLUTION: Find the x-intercept of the straight line passing through P = (2, 3) and perpendicular to y + 3x = 8 .      Log On


   

Question 397155: Find the x-intercept of the straight line
passing through P = (2, 3) and perpendicular
to
y + 3x = 8 .
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

y%2B3x=8 Start with the given equation.


y=8-3x Subtract 3x from both sides.


y=-3x%2B8 Rearrange the terms.


We can see that the equation y=-3%2Ax%2B8 has a slope m=-3 and a y-intercept b=8.


Now to find the slope of the perpendicular line, simply flip the slope m=-3 to get m=-1%2F3. Now change the sign to get m=1%2F3. So the perpendicular slope is m=1%2F3.


Now let's use the point slope formula to find the equation of the perpendicular line by plugging in the slope m=1%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=%281%2F3%29%28x-2%29 Plug in m=1%2F3, x%5B1%5D=2, and y%5B1%5D=3


y-3=%281%2F3%29x%2B%281%2F3%29%28-2%29 Distribute


y-3=%281%2F3%29x-2%2F3 Multiply


y=%281%2F3%29x-2%2F3%2B3 Add 3 to both sides.


y=%281%2F3%29x%2B7%2F3 Combine like terms. note: If you need help with fractions, check out this solver.


So the equation of the line perpendicular to 3x%2By=8 that goes through the point is y=%281%2F3%29x%2B7%2F3.


Here's a graph to visually verify our answer:


Graph of the original equation y=-3%2Ax%2B8 (red) and the perpendicular line y=%281%2F3%29x%2B7%2F3 (green) through the point .


If you need more help, email me at jim_thompson5910@hotmail.com

Also, feel free to check out my tutoring website

Jim