Question

find the equation of the line that is parellel to the line y=2x+6 and passes through the line (-9,-5)

Answer 1

2x -y+13=0

Explanation:

the given equation of the line is ,

`\implies \rm y = 2x + 6`

as we know that the slope of parallel lines are same so the line parallel to the given line will have the same slope as the given line . Comparing it to slope intercept form of the line we have ,

`\implies \rm m = 2 \ (slope)`

Now we may use the point slope form of the line to find out the equation of the line as ,

`\implies \rm y - y_1 = m(x-x_1)\\`

`\implies \rm y -(-5) =2\{ x -(-9)\}\\`

`\implies \rm y +5 = 2(x+9)\\`

`\implies \rm y +5 = 2x +18\\`

`\implies \rm 2x -y+18-5=0\\`

`\implies \rm 2x - y +13=0`

And we are done!

-Rishabh