2x + 5y = -15 is the standard form of equation
Solution:
Given that,
The point slope form of the equation of the line that passes through (-5, -1) and (10, -7) is given by:
[tex]y + 7 = \frac{-2}{5}(x-10)[/tex]
We have to write the standard form of the equation
The standard form of an equation is Ax + By = C
In this kind of equation, x and y are variables and A, B, and C are integers
Let us convert the given equation into standard form
[tex]y + 7 = \frac{-2}{5}(x-10)\\\\\text{Simplify the right hand side of equation }\\\\y + 7 = \frac{-2x}{5}+\frac{20}{5}\\\\y + 7 = \frac{-2x +20}{5}\\\\5(y+7) = -2x + 20\\\\\text{Simplify the left hand side of equation }\\\\5y + 35 = -2x + 20\\\\\text{Move the variables to left side of equation and constants to right side }\\\\2x + 5y = 20 - 35\\\\2x + 5y = -15[/tex]
Thus the standard form of equation is found
