Answer:
[tex]-5x-6y=10[/tex] ← in standard form
Step-by-step explanation:
The equation of a line in standard form is.
[tex]Ax+By=C[/tex]
were
As the equation in point-slope form
[tex]y-y_1=m\left(x-x_1\right)[/tex]
where m is the slope and [tex]\left(x_1,\:y_1\right)[/tex] is a point on the line.
as
[tex]\mathrm{Slope\:between\:two\:points}:\quad \mathrm{Slope}=\frac{y_2-y_1}{x_2-x_1}[/tex]
[tex]\left(x_1,\:y_1\right)=\left(-2,\:0\right),\:\left(x_2,\:y_2\right)=\left(-8,\:5\right)[/tex]
[tex]m=\frac{5-0}{-8-\left(-2\right)}[/tex]
[tex]m=-\frac{5}{6}[/tex]
using [tex]m=-\frac{5}{6}[/tex] and [tex]\left(x_1,\:y_1\right)=\left(-2,\:0\right)[/tex] then
[tex]y-0=-\frac{5}{6}\left(x-\left(-2\right)\right)[/tex]
[tex]-\frac{5}{6}\left(x-\left(-2\right)\right)=y-0[/tex]
[tex]6\left(-\frac{5}{6}\left(x-\left(-2\right)\right)\right)=6y[/tex]
[tex]-5\left(x+2\right)=6y[/tex]
[tex]-5x-10=6y[/tex]
[tex]-5x-6y=10[/tex] ← in standard form
