What is the equation of the line in standard form?

Answer:3x + 5y = 1Step-by-step explanation:the equation of a line in standard form isAx + By = C ( A is a positive integer and B, C are integers )Obtain the equation in slope- intercept formy = mx + c ( m is the slope and c the y-intercept )to calculate m use the gradient formulam = ( y₂ - y₁ ) / ( x₂ - x₁ )with (x₁, y₁ ) = (- 3, 2) and (x₂, y₂ ) = (2, - 1) ← 2 points on the linem = [tex]\frac{-1-2}{2+3}[/tex] = - [tex]\frac{3}{5}[/tex] y = - [tex]\frac{3}{5}[/tex] x + c ← is the partial equationto find c substitute either of the 2 points into the partial equationusing (2, - 1), then- 1 = - [tex]\frac{6}{5}[/tex] + c ⇒ c = - 1 + [tex]\frac{6}{5}[/tex] = [tex]\frac{1}{5}[/tex]y = - [tex]\frac{3}{5}[/tex] x + [tex]\frac{1}{5}[/tex] ← in slope-intercept formmultiply all terms by 55y = - 3x + 1 ( add 3x to both sides )3x + 5y = 1 ← in standard form