SOLUTION: how do I write the slope intercept form of an equation of the line that passes through the given point and is perpendicular to the graph of the following equation (-4,-3),4x+y=7

Algebra ->  Graphs -> SOLUTION: how do I write the slope intercept form of an equation of the line that passes through the given point and is perpendicular to the graph of the following equation (-4,-3),4x+y=7      Log On


   

Question 253690: how do I write the slope intercept form of an equation of the line that passes through the given point and is perpendicular to the graph of the following equation (-4,-3),4x+y=7
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

4x%2By=7 Start with the given equation.


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


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


We can see that the equation y=-4%2Ax%2B7 has a slope m=-4 and a y-intercept b=7.


Now to find the slope of the perpendicular line, simply flip the slope m=-4 to get m=-1%2F4. Now change the sign to get m=1%2F4. So the perpendicular slope is m=1%2F4.


Now let's use the point slope formula to find the equation of the perpendicular line by plugging in the slope m=1%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--3=%281%2F4%29%28x--4%29 Plug in m=1%2F4, x%5B1%5D=-4, and y%5B1%5D=-3


y--3=%281%2F4%29%28x%2B4%29 Rewrite x--4 as x%2B4


y%2B3=%281%2F4%29%28x%2B4%29 Rewrite y--3 as y%2B3


y%2B3=%281%2F4%29x%2B%281%2F4%29%284%29 Distribute


y%2B3=%281%2F4%29x%2B1 Multiply


y=%281%2F4%29x%2B1-3 Subtract 3 from both sides.


y=%281%2F4%29x-2 Combine like terms.


So the equation of the line perpendicular to 4x%2By=7 that goes through the point is y=%281%2F4%29x-2.


Here's a graph to visually verify our answer:


Graph of the original equation y=-4%2Ax%2B7 (red) and the perpendicular line y=%281%2F4%29x-2 (green) through the point .