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[tex]▪▪▪▪▪▪▪▪▪▪▪▪▪  {\huge\mathfrak{Answer}}▪▪▪▪▪▪▪▪▪▪▪▪▪▪[/tex]

The Correct choice is :

  • [tex]y = \dfrac{3}{5} x + 2[/tex]

Explanation :

As per given in the question, both the lines are parallel so they have equal slopes. that is slope of required line is :

  • [tex] \dfrac{3}{5} [/tex]

now, let's use slope and the coordinates of the given points to find the equation of line in point - slope form :

  • [tex]y - y1 = m(x - x1)[/tex]

  • [tex](y - ( - 1)) = \dfrac{3}{5} (x - ( - 5))[/tex]

  • [tex]y + 1 = \dfrac{3}{5} (x + 5)[/tex]

  • [tex]5(y + 1) = 3(x + 5)[/tex]

  • [tex]5y + 5 = 3x + 15[/tex]

  • [tex]5y = 3x + 15 - 5[/tex]

  • [tex]5y = 3x + 10[/tex]

  • [tex]y = \dfrac{3x + 10}{5} [/tex]

  • [tex]y = \dfrac{3}{5} x + 2[/tex]

therefore , the correct choice is A

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