What is the equation of the straight line passing through (4,1) which is parallel to the line given?

Slope is rise over run. Run is horizontal distance, left to right. Run is always positive because we always go left to right. Rise is the vertical change in that same distance. A negative rise means it drops.

3x + 2y = 12 We want this in the form y = mx + b. The rule is you can do any valid operation on both sides of an equation and it will still be equal. Subtract 3x.

2y = -3x + 12 Divide by 2.

y = -3x/2 + 12 Notice that I did not write -3/2x. That would be ambiguous. You can not expect a reader to guess what you meant to write.

Anyway, we now have the given slope, -3/2. The equation of a line is y = mx where m is the slope. That line passes through the origin. If you want it to pass through some point (a, b) you subtract the coordinates like this: y - b = m(x - a). That is the point-slope form, and you can rewrite it in other forms if it is convenient. You may do this with any point on the line. They all reduce to the same equation.

y - 1 = (-3/2)(x - 4) Evaluate.

y - 1 = -3x/2 + 6

y = -3x/2 + 7 <-- ANSWER I will leave it to you to prove this is equal to one of the options.