For this case we have that by definition, the standard form of a linear equation is:
[tex]ax + by = c[/tex]
We have the following equation of the point-slope form:
[tex]y + 7 = - \frac {2} {5} (x-10)[/tex]
We manipulate the equation algebraically to convert it to the standard form:
We apply distributive property to the terms within parentheses, taking into account that:
[tex]- * + = -\\- * - = +\\y + 7 = - \frac {2} {5} x + \frac {2} {5} (10)\\y + 7 = - \frac {2} {5} x + 4[/tex]
We subtract 4 from both sides of the equation:
[tex]y + 7-4 = -\frac {2} {5}x\\y + 3 = - \frac {2} {5}x[/tex]
We multiply by 5 on both sides of the equation:
[tex]5 (y + 3) = - 2x\\5y + 15 = -2x[/tex]
Adding 2x to both sides of the equation:
[tex]2x + 5y + 15 = 0[/tex]
Subtracting 15 from both sides of the equation:[tex]2x + 5y = -15[/tex]
Thus, the standard form of the equation is: [tex]2x + 5y = -15[/tex]
Answer:
Option C
