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 find an equation of the liner through (-78,-56) paralled with the line given by -8+52x+97y=0

Guest Jul 14, 2017

Best Answer 

 #1
avatar+4060 
+1

Parallel lines have the same slope. We can find the slope of our line by finding the slope of the line

 

-8 + 52x + 97y  =  0           . Let's get this into slope intercept form. Subtract  97y  from both sides.

 

-8 + 52x  =  -97y                Divide through by  -97  .

 

\(\frac{8}{97}-\frac{52}{97}x=y \)                  Rearrange.

 

\(y=-\frac{52}{97}x+\frac8{97}\)               When the equation is in this form, we can see that the slope is  -\(\frac{52}{97}\)  .

 

So, the equation of the line with a slope of  -\(\frac{52}{97}\)  that passes through  (-78, -56)  is.....

 

y - -56  =   -\(\frac{52}{97}\)( x - -78 )

 

y + 56  =   -\(\frac{52}{97}\)( x + 78 )           This is in  " point-slope "  form. We can get it in slope-intercept form.

 

y + 56  =   -\(\frac{52}{97}\)x  -  \(\frac{4056}{97}\)          Subtract  56  from both sides of this equation.

 

y  =   -\(\frac{52}{97}\)x  -  \(\frac{9488}{97}\)

 

Here's the graph I used to check this answer:  https://www.desmos.com/calculator/ssvwvuf0cb

hectictar  Jul 15, 2017
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1+0 Answers

 #1
avatar+4060 
+1
Best Answer

Parallel lines have the same slope. We can find the slope of our line by finding the slope of the line

 

-8 + 52x + 97y  =  0           . Let's get this into slope intercept form. Subtract  97y  from both sides.

 

-8 + 52x  =  -97y                Divide through by  -97  .

 

\(\frac{8}{97}-\frac{52}{97}x=y \)                  Rearrange.

 

\(y=-\frac{52}{97}x+\frac8{97}\)               When the equation is in this form, we can see that the slope is  -\(\frac{52}{97}\)  .

 

So, the equation of the line with a slope of  -\(\frac{52}{97}\)  that passes through  (-78, -56)  is.....

 

y - -56  =   -\(\frac{52}{97}\)( x - -78 )

 

y + 56  =   -\(\frac{52}{97}\)( x + 78 )           This is in  " point-slope "  form. We can get it in slope-intercept form.

 

y + 56  =   -\(\frac{52}{97}\)x  -  \(\frac{4056}{97}\)          Subtract  56  from both sides of this equation.

 

y  =   -\(\frac{52}{97}\)x  -  \(\frac{9488}{97}\)

 

Here's the graph I used to check this answer:  https://www.desmos.com/calculator/ssvwvuf0cb

hectictar  Jul 15, 2017

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