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

 Aug 24, 2018
 #1
avatar+100519 
+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

 

 

cool cool cool

 Aug 24, 2018
 #2
avatar+814 
+2

Thank you, CPhill!

mathtoo  Aug 24, 2018

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