Question

which equation represents a line that includes the points(2,-2) and (6,-4)

Answer 1

The equation represents a line that includes the points(2,-2) and (6,-4) is $y=\frac{-1}{2} x-1$

Solution:

Given that two points are (2, -2) and (6, -4)

We have to find the equation of line containing these points

The equation of line with points $(x_1, y_1)$ and $(x_2, y_2)$ is given as:

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

Where "m" is the slope of line

The slope of line "m" is given as:

$m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}$

$\text {Here } x_{1}=2 ; y_{1}=-2 ; x_{2}=6 ; y_{2}=-4$

Substituting the values in slope formula we get,

$\begin{array}{l}{m=\frac{-4-(-2)}{6-2}} \\\\ {m=\frac{-4+2}{4}=\frac{-2}{4}=\frac{-1}{2}}\end{array}$

The required equation is given as:

Substitute "m" value in equation of line formula

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

$\begin{array}{l}{y-(-2)=\frac{-1}{2}(x-2)} \\\\ {y+2=\frac{-1}{2}(x-2)}\end{array}$

$\begin{array}{l}{y+2=\frac{-1}{2} x+1} \\\\ {y=\frac{-1}{2} x-1}\end{array}$

Thus the equation of line is found out