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

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Write an equation of the line passing through

dyp

11.03.2022

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.

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