Question

How do you write an equation in standard form for a line passes through (2, –3) and is perpendicular to y = 4x + 7?

Answer 1

Answer: the equation of the line is `y=-1/4x -5/2`

Explanation: We have two lines: `L_1` defined by the equation `y=ax+b` and `L_2` defined by the equation `y=4x+7` `=>` The slope of the line `L_2` is `4`.

We know that, If `L_1` is perpendicular to `L_2`, then the slope of `L_1` is the inverse reciprocal of the slope of `L_2`. Therefore, the slope of `L_1` is `-1/4`.

So, the equation of `L_1` is `-1/4x + b`

The line `L_1` contains the point `A(2,-3)`, therefore we have the following equation: `-3=-1/4*2+b` `=>` `b=-5/2`

Therefore, the equation of `l_1` is `y=-1/4x -5/2`