SOLUTION: Write an equation in slope-intercept form of the line that passes through the given point and is perpendicular to the graph of each equation. 4x-3y=7; (5, -2)

Algebra ->  Linear-equations -> SOLUTION: Write an equation in slope-intercept form of the line that passes through the given point and is perpendicular to the graph of each equation. 4x-3y=7; (5, -2)      Log On


   

Question 243550: Write an equation in slope-intercept form of the line that passes through the given point and is perpendicular to the graph of each equation.
4x-3y=7; (5, -2)
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

4x-3y=7 Start with the given equation.


-3y=7-4x Subtract 4x from both sides.


-3y=-4x%2B7 Rearrange the terms.


y=%28-4x%2B7%29%2F%28-3%29 Divide both sides by -3 to isolate y.


y=%28%28-4%29%2F%28-3%29%29x%2B%287%29%2F%28-3%29 Break up the fraction.


y=%284%2F3%29x-7%2F3 Reduce.


We can see that the equation y=%284%2F3%29x-7%2F3 has a slope m=4%2F3 and a y-intercept b=-7%2F3.


Now to find the slope of the perpendicular line, simply flip the slope m=4%2F3 to get m=3%2F4. Now change the sign to get m=-3%2F4. So the perpendicular slope is m=-3%2F4.


Now let's use the point slope formula to find the equation of the perpendicular line by plugging in the slope m=-3%2F4 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%2F4%29%28x-5%29 Plug in m=-3%2F4, x%5B1%5D=5, and y%5B1%5D=-2


y%2B2=%28-3%2F4%29%28x-5%29 Rewrite y--2 as y%2B2


y%2B2=%28-3%2F4%29x%2B%28-3%2F4%29%28-5%29 Distribute


y%2B2=%28-3%2F4%29x%2B15%2F4 Multiply


y=%28-3%2F4%29x%2B15%2F4-2 Subtract 2 from both sides.


y=%28-3%2F4%29x%2B7%2F4 Combine like terms. note: If you need help with fractions, check out this solver.


So the equation of the line perpendicular to 4x-3y=7 that goes through the point is y=%28-3%2F4%29x%2B7%2F4.


Here's a graph to visually verify our answer:


Graph of the original equation y=%284%2F3%29x-7%2F3 (red) and the perpendicular line y=%28-3%2F4%29x%2B7%2F4 (green) through the point .