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Step-by-step explanation:
The x-intercept is at (-3, 0). To find the slope of the perpendicular line, let's rewrite the equation to its slope-intercept form, which is
y = (2/3)x + 2
This means that the perpendicular line has a slope m = -3/2. So the slope-intercept form of this new line is
y = -(3/2)x + k. Since this line passes through (-3, 0), we cal solve for k:
0 = -(3/2)(-3) + k or k = -9/2
So our equation becomes (slope-intercept form)
or in its standard form,