+816 What is the x-intercept of the line perpendicular to the line defined by \(3x-2y = 6\) and whose y-intercept is 2?
+128475 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
