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Find equation through line

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

Jul 14, 2017

#1
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+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

Jul 15, 2017

#1
+7348
+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