Find the equation of the line through (5,7) parallel to the line 7x + 5y = 12 

m\(_1\) = m\(_2\)  condition for parallelism

From 7x + 5y = 12 

5y = -7x + 12

y = \(\frac{-7x}{5}\) + \(\frac{12}{5}\)

m\(_1\) = \(\frac{-7}{5}\) =  m\(_2\)

equation of the line = y - y\(_1\) =  m\(_2\)[x - x\(_1\)]

y - 7 =  \(\frac{-7}{5}\)[x - 5]

5(y - 7) = -7(x - 5)

5y - 35 = -7x + 35

5y + 7x = 35 + 35

5y + 7x = 70