SOLUTION: please explain to me: find an equation of the line that has x-intercept (2,0) and is perpendiclar to 4x+3y=6

Algebra ->  Graphs -> SOLUTION: please explain to me: find an equation of the line that has x-intercept (2,0) and is perpendiclar to 4x+3y=6      Log On


   

Question 737772: please explain to me: find an equation of the line that has x-intercept (2,0) and is perpendiclar to 4x+3y=6
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
First realize that ANY line which is perpendicular to thr given
line will have the same slope, so that is the 1st thing to find.
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The equation +4x+%2B+3y+=+6+ is in the standard form. Put
it into the slope-intercept form which is +y+=+m%2Ax+%2B+b+
The +m+ will be the slope of this line.
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+4x+%2B+3y+=+6+
+3y+=+-4x+%2B+6+
+y+=+%28-4%2F3%29%2Ax+%2B+2+
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+m+=+-4%2F3+
Now find the slope that is perpendicular to this slope
The formula is +m%5Bp%5D+=+-1+%2F+m+, so
+m%5Bp%5D+=+-1+%2F+%28-4%2F3%29+
+m%5Bp%5D+=+3%2F4+
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So far, you have:
+y+=+%283%2F4%29%2Ax+%2B+b+
You just need to find +b+
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You given the point (2,0) also, so just plug this x and y
into the equation and solve for +b+
+0+=+%283%2F4%29%2A2+%2B+b+
+0+=+3%2F2+%2B+b+
+b+=+-3%2F2+
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The complete equation is:
+y+=+%283%2F4%29%2Ax+-+3%2F2+
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Check:
does it go through (2,0)?
+y+=+%283%2F4%29%2Ax+-+3%2F2+
+0+=+%283%2F4%29%2A2+-+3%2F2+
+%283%2F4%29%2A2+=+6%2F4+
+6%2F4+=+6%2F4+
OK
Here is the plot of both lines: