The require line is passing through the points [tex](-6,-5)[/tex] and [tex](-4,-3)[/tex].
We can use the following formula to find the equation of the line passing through a pair of points:
[tex]y-y_1=m(x-x_1)[/tex] .................equation (1)
Where 'm' is slope of the line which is defined as:
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]
Now, lets say point [tex](x_1, y_1)[/tex] is [tex](-6,-5)[/tex] and point [tex](x_2,y_2)[/tex] is [tex](-4,-3)[/tex].
We will calculate the slope of the line now:
[tex]m=\frac{-3-(-5)}{-4-(-6)} =\frac{-3+5}{-4+6} =\frac{2}{2} =1[/tex]
So, the slope of the required line is 1.
Now, plugging the value of the slope in equation 1, we get:
[tex]y-(-5)=1(x-(-6))[/tex]
[tex]y+5=x+6[/tex]
[tex]y=x+6-5[/tex]
[tex]y=x+1[/tex]
Therefore, the equation of the line passing through the points [tex](-6,-5)[/tex] and [tex](-4,-3)[/tex] is [tex]y=x+1[/tex].
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:
[tex]-5=-6+1=-5[/tex]
Hence, the equation of the line is correct.
