Question

Find the line equation Parallel to y = -3x - 1 and passing through the point (2,-3)

Answer 1

The equation of the given line is,

`y=-3x-1\text{ ------(1)}`

We have to find the equation of a line parallel to y=-3x-1 and passing through the point (x1, y1)=(2, -3).

The general equation of a line is,

`y=mx+c\text{ ------(2)}`

Here, m is the slope of the line.

Comparing equations (1) and (2), we find that the slope of the line y=-3x-1 is m=-3.

The slope of two parallel lines are always equal. Hence, the slope of a line parallel to the line y=-3x-1 is also m=-3.

Now, the formula for the point slope form of the equation of a line can be written as,

`y-y1=m(x-x1)`

Substitute m=-3, x1=2 and y1=-3 in the above equation to find the equation of a line paralle to y=-3x-1 and passing through point (2, -3) is,

`\begin{gathered} y-(-3)=-3(x-2) \\ y+3=-3x-3*(-2) \\ y+3=-3x+6 \\ y=-3x+6-3 \\ y=-3x+3 \end{gathered}`

Therefore, the equation of a line paralle to y=-3x-1 and passing through point (2, -3) is y=-3x+3.