Question

Determine the equation of a line that is perpendicular to the line 2x + 3y = 7 and passes through the point (0,6).

Answer 1

If a line is Perpendicular to another it means that the slopes are the negative reciprocals of each other. So the slope of the given line is -2/3 so the slope of the new line is going to be 3/2. Now you have a slope of 3/2 and a point (0,6) use the point-slope formula \[y - y1 = m (x - x1)\] and solve for y

Answer 2

2x + 3y = 7 and passes through the point (0,6).
2x + 3y =7
-2x
3y=-2x+7
divide both sides by 3
y= -2/3x +7/3

y - 6 = -2/3(0) = 7
+6 +6
y= 13

So, y= -2/3x +13 is the equation of the line.
That means that they are not perpendicular!