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

Guest Jul 14, 2017

#1**+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

#1**+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