Write an equation of a line in POINT SLOPE FORM that is PERPINDICULAR to the line y=2x+1 and passes through the point (1,-2)

Answer 1

To write an equation of a line in point slope form that is perpendicular to the line y = 2x + 1 and passes through the point (1, -2), we first need to find the slope of the line y = 2x + 1. The slope of a line is given by the formula m = (y2 - y1)/(x2 - x1), where (x1, y1) and (x2, y2) are two points on the line. Plugging in the values, we find that the slope of the line y = 2x + 1 is m = 2.

A line is perpendicular to another line if the slope of the first line is the negative reciprocal of the slope of the second line. In other words, if the slope of the first line is m1, then the slope of the second line is -1/m1.

Since the slope of the line y = 2x + 1 is 2, the slope of the line we want to find is -1/2. We can use the point slope form of a line, which is y - y1 = m(x - x1), to write an equation for the line. Plugging in the values, we get:

y - (-2) = (-1/2)(x - 1)

y + 2 = -(1/2)(x - 1)

y + 2 = -1/2x + 1/2

2x + y = -1/2

This is the equation of the line in point slope form that is perpendicular to the line y = 2x + 1 and passes through the point (1, -2).

Answer 2

y=2x+1 has slope 2 = the coefficient of the x term

a perpendicular line has a negative inverse slope = -1/2

the equation of the perpendicular line through (1,-2) is

y -(-2) = (-1/2)(x-1) in point slope form