Perpendicular to y=2x+3 through (2, - 3)

Hello!

To find the line perpendicular to the given line, y = 2x + 3, firstly, find the slope of the perpendicular line. To find it, use this format: - 1/m, where m is the slope. It is also called the "negative reciprocal" of the slope of the given line.

Then, you substitute an ordered pair into a new slope-intercept equation (with the slope) and find the y-intercept.

-1/m when m = 2 → - 1/2

y = - 1/2x + b (substitute the given ordered pair)

-3 = - 1/2 (2) + b (simplify)

-3 = - 1 + b (add 1 to both sides)

-2 = b | The y-intercept of the perpendicular equation is - 2.

Therefore, the line perpendicular to the given equation, that also goes through the given ordered pair is y = - 1/2x - 2.