Question

which of the following are the equations for the line shown

Answer 1

Solution

Two points on the line are (-3,3) and (-1,-3)

The equation of a straight line given two points can be calculated by the formula

$\begin{gathered} \frac{y-y_1}{x-x_1}=\frac{y_2-y_1}{x_2-x_1} \\ \\ \text{Where (x}_1,y_1)=(-3,3)and(x_2,y_2)=(-1,-3) \end{gathered}$

By substituting into the formula above, we have

$\begin{gathered} \frac{y-3}{x-(-3)}=\frac{-3-3}{-1-(-3)} \\ \frac{y-3}{x+3}=\frac{-6}{-1+3} \\ \frac{y-3}{x+3}=\frac{-6}{2} \\ \frac{y-3}{x+3}=-3 \\ y-3=-3(x+3) \\ \end{gathered}$

The first correct choice is y-3 = -3(x+3)

Looking at the options given, we can also write the equation in another form by adding 6 to both sides

$\begin{gathered} y-3=-3(x+3) \\ \text{add 6 to both sides} \\ y-3+6=-3(x+3)+6 \\ y+3=-3x-9+6 \\ y+3=-3x-3 \\ y+3=-3(x+1) \end{gathered}$

The second correct choice is y+3 = -3(x+1)

Hence, Option A and option B are the correct options