SOLUTION: The line through (2,-3) that is perpendicular to the line y= -4x + 8 written in standard form containing only integer coefficients. I am having a horrible time with these graphs,

Algebra ->  Graphs -> SOLUTION: The line through (2,-3) that is perpendicular to the line y= -4x + 8 written in standard form containing only integer coefficients. I am having a horrible time with these graphs,       Log On


   

Question 181883: The line through (2,-3) that is perpendicular to the line y= -4x + 8 written in standard form containing only integer coefficients. I am having a horrible time with these graphs, any help is greatly appreciated!
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

We can see that the equation y=-4%2Ax%2B8 has a slope m=-4 and a y-intercept b=8.


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=-4 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-2%29 Plug in m=1%2F4, x%5B1%5D=2, and y%5B1%5D=-3


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


4%28y%2B3%29=x-2 Multiply both sides by 4.


4y%2B12=x-2 Distribute


4y=x-2-12 Subtract 12 from both sides.


4y-x=-2-12 Subtract "x" from both sides.


4y-x=-14 Combine like terms.


-x%2B4y=-14 Rearrange the terms.


x-4y=14 Multiply EVERY term by -1 to make the "x" coefficient positive.


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Answer:

So the equation of the line that is perpendicular to y=-4%2Ax%2B8 and goes through the point (2,-3) in standard form is x-4y=14



Here's the graph of the two lines to verify the answer:


Graph of the original equation y=-4%2Ax%2B8 (red) and the perpendicular line x-4y=14 (green) through the point .