What is an equation of the line that passes through the point (5,−2) and is parallel to the line 2x-5y=35?

Find the slope of the given line

If we put the line 2x - 5y = 35 into the y = mx + c form, the coefficient of x (m) is the slope.

                           since     2x - 5y = 35

                               ⇒              5y = 2x - 35

                                                   y = ²/₅ x - 7

                  ∴      the slope of the line is ²/₅

Identify the slope of the parallel line

When two lines are parallel, they have the same slope.

              ∴ the slope of the parallel is also ²/₅  

Determine the equation of the parallel line

We can now use the point-slope form (y - y₁) = m(x - x₁)) to write the equation for this line where (x₁ , y₁) is (5,−2) :    

                             y - (-2)  =  ²/₅   (x - 5)

                              y + 2 = ²/₅   (x - 5)

If we were to write the equation in the same form as the line that was given:

                                 since  y + 2 = ²/₅   (x - 5)

                                                  y =  ²/₅  x - 2 - 2

                                      y -  ²/₅  x  = - 4      [multiply through by 5]

                                         5y - 2x = -20

To test my answer, I have included a Desmos Graph that I graphed using the information provided in the question and my answer.

i'm pretty sure it's 477,585,296, but perhaps my math is incorrect.