Find the equation of the line parallel to 2y = 3(x - 2) and passes through the point (2, 3)

Analyze the question: We need a line parallel to 2y = 3(x − 2) that passes through (2, 3). Parallel lines have the same gradient (slope).

Concept: A line in the form y = mx + c has gradient m. Parallel lines share the same m.

Step 1: Find the gradient of the given line

2y = 3(x − 2) 2y = 3x − 6 y = (3/2)x − 3

So the gradient is m = 3/2.

Step 2: Use the same gradient with the point (2, 3)

y − y₁ = m(x − x₁) y − 3 = (3/2)(x − 2) y − 3 = (3/2)x − 3 y = (3/2)x

Step 3: Check with the point

When x = 2: y = (3/2)(2) = 3 ✓

Check the options:

• A and B have gradient 2/3, which is wrong (this is the reciprocal, a common trap).
• D has gradient −2/3, which is also wrong.
• C: y = (3/2)x has gradient 3/2 and passes through (2, 3). ✓

Tip: For "parallel" questions, first rewrite the given line as y = mx + c to read off m, then keep that same m. Don't flip the fraction (that is for perpendicular lines, where you also change the sign, so m₁ × m₂ = −1). Always check your final equation by substituting the given point.