Answer :
ANSWER
[tex]2y+x+16=0[/tex]EXPLANATION
We want to find the equation of the line in general form i.e.:
[tex]Ax+By+C=0[/tex]where A, B, C are constants
To do this, we have to first find the slope of the line using the formula:
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]where (x1, y1) and (x2, y2) are the two points the line passes through.
We have that the two points are (4, -1) and (-2, -7)
Therefore, the slope of the line is:
[tex]\begin{gathered} m=\frac{-7-(-10)}{-2-4} \\ m=\frac{-7+10}{-2-4} \\ m=\frac{3}{-6} \\ m=-\frac{1}{2} \end{gathered}[/tex]Now, we find the equation of the line in point-slope form by using the formula:
[tex]y-y_1=m(x-x_1)[/tex]Therefore, we have:
[tex]\begin{gathered} y-(-10)=-\frac{1}{2}(x-4) \\ y+10=-\frac{1}{2}x+2 \end{gathered}[/tex]To express it in the general form, first, eliminate the fraction by multiplying both sides of the equation by 2:
[tex]2y+20=-x+4[/tex]Now, take all the terms to the left side of the equation:
[tex]\begin{gathered} 2y+x+20-4=0 \\ 2y+x+16=0 \end{gathered}[/tex]That is the equation of the line in the general form.