Question

Write an equation of the line passing through each of the following pairs of points. g (−6, −5), (−4, −3)

Answer 1

The require line is passing through the points $(-6,-5)$ and $(-4,-3)$.

We can use the following formula to find the equation of the line passing through a pair of points:

$y-y_1=m(x-x_1)$ .................equation (1)

Where 'm' is slope of the line which is defined as:

$m=\frac{y_2-y_1}{x_2-x_1}$

Now, lets say point $(x_1, y_1)$ is $(-6,-5)$ and point $(x_2,y_2)$ is $(-4,-3)$.

We will calculate the slope of the line now:

$m=\frac{-3-(-5)}{-4-(-6)} =\frac{-3+5}{-4+6} =\frac{2}{2} =1$

So, the slope of the required line is 1.

Now, plugging the value of the slope in equation 1, we get:

$y-(-5)=1(x-(-6))$

$y+5=x+6$

$y=x+6-5$

$y=x+1$

Therefore, the equation of the line passing through the points $(-6,-5)$ and $(-4,-3)$ is $y=x+1$.

To verify if the equation of line is correct or not, you can plug in any of the points in the equation and compare both the sides:

Lets plug in  (-6,-5) in the equation:

$-5=-6+1=-5$

Hence, the equation of the line is correct.