Answer:
Option 2, y=-3/2x-4
Explanation:
Solve with the point-slope formula: y-y1=m(x-x1). The line is perpendicular, meaning the slope of the new equation will be the oppposite reciprocal of the original slope.
First, we need to rewrite the original equation into standard form.
2x-3y=13
-3y=13-2x
y=-13/3+2/3x
From this, we can see that the slope here is 2/3. Since the line we're looking for is perpendicular, the opposite reciprocal of that slope is -3/2.
Now, we can plug in the coordinates we have into the formula (-6, 5), along with our slope (-3/2).
y-(5)=-3/2(x+6)
y-5=-3/2x-9
y=-3/2x-4
And to check, we can just plug the coordinates into our new equation:
Check:
(5)=-3/2(-6)-4
5=9-4
5=5