Question

Which equation represents the line that passes through points B and C on the graph?

Answer 1

Answer:

Therefore, the equation represents the line that passes through points B and C on the graph will be:

                                             $y=-2x-6$

Step-by-step explanation:

From the diagram, it is clear that

• the point B is (-4, 2)

• the point C is (-2, -2)

$\mathrm{Slope\:between\:two\:points}:\quad \mathrm{Slope}=\frac{y_2-y_1}{x_2-x_1}$

$\left(x_1,\:y_1\right)=\left(-4,\:2\right),\:\left(x_2,\:y_2\right)=\left(-2,\:-2\right)$

$m=\frac{-2-2}{-2-\left(-4\right)}$

$m=-2$

Substituting $m = -2$ and $\left(x_1,\:y_1\right)=\left(-4,\:2\right)$ in the point slope form

$y-y_1=m\left(x-x_1\right)$

Thus the equation of line becomes

$y-2=-2\left(x-\left(-4\right)\right)$

$y-2=-2\left(x+4\right)$

$y-2=-2x-8$

$y=-2x-6$

Therefore, the equation represents the line that passes through points B and C on the graph will be:

                                             $y=-2x-6$