SOLUTION: write the equation of the line that passes through (3,2) and is perpendicular to the line 5x+4y=11

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Question 54979: write the equation of the line that passes through (3,2) and is perpendicular to the line 5x+4y=11
Answer by funmath(2933) About Me  (Show Source):
You can put this solution on YOUR website!
write the equation of the line that passes through (3,2) and is perpendicular to the line 5x+4y=11
First, we need to find the slope of the line they gave us. To do this we need to put the equation in slope intercept form highlight%28y=mx%2Bb%29, where m=slope, and (0,b)=y-intercept.
5x%2B4y=11
-5x%2B5x%2B4y=-5x%2B11
4y=-5x%2B11
4y%2F4=-5x%2F4%2B11%2F4
y=%28-5%2F4%29x%2B11%2F4
y=highlight%28-5%2F4%29x%2B11%2F4 the slope of this line is -5/4.
We need a line perpendicular to this line so our slope needs to be 4/5. (Flip the slope and change the sign.)
Now we use the point slope formula highlight%28y-y1=m%28x-x1%29%29, where m=slope and (x1,y1)=the given point. Our m=4/5 and our point is (x1,y1)=(3,2)
y-2=%284%2F5%29%28x-3%29
5%28y-2%29=5%284%2F5%29%28x-3%29
5y-10=%2820%2F5%29%28x-3%29
5y-10=4%28x-3%29
5y-10=4x-12
5y-10%2B10=4x-12%2B10
5y=4x-2
5y%2F5=4x%2F5-2%2F5
y=%284%2F5%29x-2%2F5 <--slope intercept form of a line highlight%28y=mx%2Bb%29
Happy Calculating!!!