What is the x-intercept of the line perpendicular to the line defined by \(3x-2y = 6\) and whose y-intercept is 2?

mathtoo
Aug 24, 2018

#1**+2 **

3x - 2y = 6 rearrange as

3x - 6 = 2y divide through by 2

(3/2)x - 3 = y

A line perpendicular to this will have a slope of (-2/3)

If this line has a y intercept of 2, then the point (0,2) is on the graph

So......the equation of the line is

y = (-2/3)x + 2

To find the x intercept, let y = 0

0 = (-2/3)x + 2

-2 = (-2/3)x

x = -2(-3/2) = 3

Here's a graph : https://www.desmos.com/calculator/fi2c8ubbdw

CPhill
Aug 24, 2018