Q8. - Algebra 1

Question

Which equation passes through the points $\mathbf{(}\mathbf{-}\mathbf{1}\mathbf{,}\mathbf{-}\mathbf{3}\mathbf{)}$ and $\mathbf{(}\mathbf{-}\mathbf{2}\mathbf{,}\mathbf{3}\mathbf{)}$.

$\mathit{F}$ $\mathit{y}\mathbf{=}\mathbf{-}\mathbf{6}\mathit{x}\mathbf{-}\mathbf{9}$

$\mathit{G}$ $\mathit{y}\mathbf{=}\mathbf{-}\frac{1}{4}\mathit{x}\mathbf{+}\mathbf{3}$
$\mathit{H}$ $\mathit{y}\mathbf{=}\mathbf{4}\mathit{x}\mathbf{-}\mathbf{5}$

$\mathit{J}$ $\mathit{y}\mathbf{=}\frac{2}{3}\mathit{x}\mathbf{+}\mathbf{1}$

Step-by-Step Solution

Answer

The equation that passes through the given points is $\mathit{y}\mathbf{=}\mathbf{-}\mathbf{6}\mathit{x}\mathbf{-}\mathbf{9}$.

Step 1. Find the slope.

Find the slope of the line containing the given points.

$\begin{array}{l}m=\frac{y_2-y_1}{x_2-x_1}\\ =\frac{3-(-3)}{-2-(-1)}\\ =\frac{6}{-1}\\ =-6\end{array}$

Step 2. Find y -intercept.

Use either point to find the y-intercept.

$\begin{array}{l}y=mx+b\\ -3=-6(-1)+b\\ -3=6+b\\ b=-9\end{array}$

Step 3. Write equation.

Write equation in slope intercept form.

$\begin{array}{l}y=mx+b\\ =-6x-9\end{array}$ 

Therefore, the equation is $y=-6x-9$. Option $F$ is the required answer.