Answer: The correct option is (C) [tex]2x+5y=-15.[/tex]
Step-by-step explanation: Given that the equation of the line that passes through (-5, -1) and (10, -7) in point-slope form is given by
[tex]y+7=-\dfrac{2}{5}(x-10)~~~~~~~~~~~~~~~~~~~~~~~(i)[/tex]
We are to find the standard form of the equation for the above line.
We know that the STANDARD form of the equation of a line is given by
[tex]ax+by=c,~~~~~\textup{[a and b cannot be zero at the same time]}.[/tex]
From equation (i), we have
[tex]y+7=-\dfrac{2}{5}(x-10)\\\\\Rightarrow 5(y+7)=-2(x-10)\\\\\Rightarrow 5y+35=-2x+20\\\\\Rightarrow 2x+5y=20-35\\\\\Rightarrow 2x+5y=-15.[/tex]
Thus, the required standard form is [tex]2x+5y=-15.[/tex]
Option (C) is CORRECT.
