Respuesta :

mhanifa

Answer:

  • 5x - 7y = 17

Step-by-step explanation:

Given line:

  • 5x - 7y = 8

Convert the equation into slope-intercept form:

  • 5x - 7y = 8
  • 7y = 5x - 8
  • y = 5/7x - 8/7

The line parallel to this has same slope of 5/7 and passes through the point (2, - 1).

Use point-slope form and convert the equation into standard form:

  • y - (- 1) = 5/7(x - 2)
  • y + 1 = 5/7x - 10/7
  • 7y + 7 = 5x - 10
  • 5x - 7y = 7 + 10
  • 5x - 7y = 17
  • 5x-7y=8

Isolate y

  • 7y=5x-8
  • y=5/7x-8/7

Here

  • m=5/7

Parallel lines have equal slope

Point(2,-1)

Equation of line in point slope form

[tex]\\ \sf\longmapsto y-y_1=m(x-x_1)[/tex]

[tex]\\ \sf\longmapsto y+1=5/7(x-2)[/tex]

[tex]\\ \sf\longmapsto 7y+7=5x-10[/tex]

[tex]\\ \sf\longmapsto 5x-7y-17=0[/tex]