Answer:
Therefore, the equation represents the line that passes through points B and C on the graph will be:
[tex]y=-2x-6[/tex]
Step-by-step explanation:
From the diagram, it is clear that
[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(-4,\:2\right),\:\left(x_2,\:y_2\right)=\left(-2,\:-2\right)[/tex]
[tex]m=\frac{-2-2}{-2-\left(-4\right)}[/tex]
[tex]m=-2[/tex]
Substituting [tex]m = -2[/tex] and [tex]\left(x_1,\:y_1\right)=\left(-4,\:2\right)[/tex] in the point slope form
[tex]y-y_1=m\left(x-x_1\right)[/tex]
Thus the equation of line becomes
[tex]y-2=-2\left(x-\left(-4\right)\right)[/tex]
[tex]y-2=-2\left(x+4\right)[/tex]
[tex]y-2=-2x-8[/tex]
[tex]y=-2x-6[/tex]
Therefore, the equation represents the line that passes through points B and C on the graph will be:
[tex]y=-2x-6[/tex]
