Write an equation of the line that passes through (-5,2) and is perpendicular to y+3=2x

Answer 1

The equation for a line in slope-intercept form is y = mx + b. The given equation is equivalent to

y = 2x - 3. The slope of this line is m = 2.

It is a well known fact that the product of slopes of perpendicular lines will = -1 (the 2 slopes are negative reciprocals of each other). So the perpendicular line to the given equation will have a slope = -1/2.

The new line will then have an equation of y = -x/2 + b. Plugging in the given point of (-5,2) makes the equation

2 = 5/2 + b, so b = -1/2, and the equation can be written y = -x/2 - 1/2 or y = -(1/2)(x + 1). It could also be written as x + 2y = -1