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

1 Answer
Jun 6, 2015

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