Answer:
y = (-2/3)x +1
Step-by-step explanation:
The standard equation of a line is: y=mx+b where m-is the slope, and b-is the y intercept. Rewrite the given equation in standard form.
3x+2y = 6
2y = 3x+6
y= (3/2)x+3
So the given equation has the slope m =3/2 and y-intercept= 3
A line ⊥ to the given line will have the slope negative reciprocal so the line is
y= (-2/3 )x +b
To find b will substitute the given point (6,-3) in the new found equation
-3= (-2/3 )6 +b
-3= -4 +b
-3+4 = b
1 = b
The equation of the line that is perpendicular to the graph of 3x+2y=6 and contains the point (6,-3) is y = (-2/3)x +1
