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We can solve this problem by using Two Point Form which is
 y- y_{1}=( \frac{ y_{2}- y_{1}  }{ x_{2}- x_{1}  })(x- x_{1})

The given in this problem are points (-5,7) and y-intercept 3 or (0,3).
We will let (x1,y1) as (0,3) and (x2,y2) as (-5,7).
We will just substitute this two points in the formula above.
y-3=( \frac{7-3}{-5-0})(x-0)
y-3= \frac{4}{-5} x
-5y - 3 = 4x
4x + 5y = -3    is the equation of the line in standard form