The point-slope form:
[tex]y-y_1=m(x-x_1)[/tex]
The formula of a slope:
[tex]m=\dfrac{y_2-y_1}{x_2-x_1}[/tex]
We have the points (-10, -7) and (-5, -9). Substitute:
[tex]m=\dfrac{-9-(-7)}{-5-(-10)}=\dfrac{-9+7}{-5+10}=\dfrac{-2}{5}=-\dfrac{2}{5}[/tex]
[tex]y-(-7)=-\dfrac{2}{5}(x-(-10))[/tex]
[tex]\boxed{y+7=-\dfrac{2}{5}(x+10)}[/tex] point-slope form
[tex]y+7=-\dfrac{2}{5}(x+10)[/tex] use distributive property
[tex]y+7=-\dfrac{2}{5}x-4[/tex] subtract 7 from both sides
[tex]\boxed{y=-\dfrac{2}{5}x-11}[/tex] slope-intercept form
[tex]y=-\dfrac{2}{5}x-11[/tex] multiply both sides by 5
[tex]5y=-2x-55[/tex] add 2x to both sides
[tex]\boxed{2x+5y=-55}[/tex] standard form
