SOLUTION: state the equation (in slope-intercept form) of the line that passes through (-10,8) and is perpendicular to the line y=5/2x-17

Algebra ->  Linear-equations -> SOLUTION: state the equation (in slope-intercept form) of the line that passes through (-10,8) and is perpendicular to the line y=5/2x-17      Log On


   

Question 227558: state the equation (in slope-intercept form) of the line that passes through (-10,8) and is perpendicular to the line y=5/2x-17
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

We can see that the equation y=%285%2F2%29x-17 has a slope m=5%2F2 and a y-intercept b=-17.


Now to find the slope of the perpendicular line, simply flip the slope m=5%2F2 to get m=2%2F5. Now change the sign to get m=-2%2F5. So the perpendicular slope is m=-2%2F5.


Now let's use the point slope formula to find the equation of the perpendicular line by plugging in the slope m=-2%2F5 and the coordinates of the given point .


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


y-8=%28-2%2F5%29%28x--10%29 Plug in m=-2%2F5, x%5B1%5D=-10, and y%5B1%5D=8


y-8=%28-2%2F5%29%28x%2B10%29 Rewrite x--10 as x%2B10


y-8=%28-2%2F5%29x%2B%28-2%2F5%29%2810%29 Distribute


y-8=%28-2%2F5%29x-4 Multiply


y=%28-2%2F5%29x-4%2B8 Add 8 to both sides.


y=%28-2%2F5%29x%2B4 Combine like terms.


So the equation of the line perpendicular to y=%285%2F2%29x-17 that goes through the point is y=%28-2%2F5%29x%2B4.


Here's a graph to visually verify our answer:


Graph of the original equation y=%285%2F2%29x-17 (red) and the perpendicular line y=%28-2%2F5%29x%2B4 (green) through the point .