Question

What equation is graphed in this figure?

Answer 1

Answer:

The third equation: $y+2=-3(x-1)$

Step-by-step explanation:

The two points on the line are $(-1,4)$ and $(1,-2)$.

Slope of the line passing through two points $(x_{1},y_{1})$ and $(x_{2},y_{2})$ is given as:

$m=(y_{2} -y_{1})/ (x_{2} -x_{1})$

Here, $(x_{1},y_{1})$ and $(x_{2},y_{2})$ are $(-1,4)$ and $(1,-2)$.

Therefore, slope is equal to, $m=(-2-4 )/ (1-(-1)$

                                               $m=-6/2$

                                               $m=-3$  

Now, equation of a straight line with slope m and points $(x_{1},y_{1})$ and $(x_{2},y_{2})$ is given as:

$y-y_{1}=m(x-x_{1})\\y-y_{2}=m(x-x_{2})$

Now, if we use the 2nd form, then $x_{2}=1,y_{2}=-2$.

So, the equation is given as :

$y-(-2)=-3(x-1)\\y+2=-3(x-1)$