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=(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=(-3-(-5))/(-4-(-6)) =(-3+5)/(-4+6) =(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.