Question

Given the equation y = 1/2x + 3, find the equation of the line perpendicular passing through (1, 6).

a) y = -2x + 8
b) y = 2x + 8
c) y = -2x + 3
d) y = 2x + 3

Answer 1

To find the equation of the line perpendicular to y = 1/2x + 3, use the slope-intercept form and substitute the given point to determine the equation of the line passing through it.

Step-by-step explanation:

To find the equation of the line perpendicular to y = 1/2x + 3 passing through the point (1, 6), we need to determine the slope of the perpendicular line. The slope of the given line is 1/2, therefore the slope of the perpendicular line will be -2 (negative reciprocal of 1/2).

Using the slope-intercept form of a linear equation, y = mx + b, we can substitute the known values to find the equation of the perpendicular line. The point (1, 6) gives us the value of y and x.

Substituting the values into the equation, we get y = -2x + 8.