kuvyojhmoob
  • kuvyojhmoob
Find a general form of an equation of the line through the point A that satisfies the given condition. A(3, −1); parallel to the line 9x − 2y = 4
Mathematics
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SOLVED
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chestercat
  • chestercat
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anonymous
  • anonymous
Hello @kuvyojhmoob ok so your first step is find the slope of the line...
anonymous
  • anonymous
Since it is parallel to the line: \[ 9x-2y=4 \ \ \ \ \rightarrow \ \ \ \ y=\frac{9}{2}x-2\] This means their slopes are equivalent. Thus the slope of the desired line is \[ m=\frac{9}{2}\]
anonymous
  • anonymous
Next we know it goes through the point A(3,-1) this means we can calculate the y-intercept as follows. Starting with the slope-intercept form of the equation of a line: \[y=mx+b\] and substituting in our know slope m: \[y=\frac{9}{2}x+b\] then substitute in our point (3,1) and solve for b: \[(-1)=\frac{9}{2}(3)+b \ \ \ \ \rightarrow \ \ \ \ b=-1-\frac{9*3}{2}=-(\frac{2+27}{2})=- \frac{29}{2}\] Putting it all together, the desired eqution of the line: \[y= \frac{9}{2}x-\frac{29}{2}=\frac{1}{2}(9x-29)\]

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