5. Which equation describes a line that contains the point (2,3) and is perpendicular to the
line represented by the equation 2x + 3y = 6?

y = 3x/2

Step-by-step explanation:

Let's solve for y first.

3y = -2x+6

y = -2x/3 + 2

We know that the slope is perpendicular to -2/3, meaning that we have to find the negative reciprocal of -2/3, which is 3/2.

y = 3x/2 + C.

We know the point (2, 3) and we plug that into our equation above.

3 = 3/2(2) + C.

3 = 3 + C

0 = C

C = 0.

We now plug in C for the equation, which gives us y = 3x/2.

the first option is the answer.