Final answer:
To solve the equation Y - Yi = m(X-Xi) for Y, we add Yi to both sides to isolate Y, yielding the correct equation Y = Yi + m(X - Xi), which simplifies to Y = Yi + mX.
Step-by-step explanation:
We are solving for Y in the equation Y - Yi = m(X-Xi) which is a point-slope form of the linear equation, where m represents the slope and (Yi, Xi) are the coordinates of a point through which the line passes. To find Y, we will isolate it on one side of the equation:
Y - Yi = m(X - Xi)
Add Yi to both sides:
Y = m(X - Xi) + Yi
Thus, the correct form of the equation when solved for Y is Y = mX + Yi - mXi which simplifies to Y = Yi + m(X - Xi). Due to the distributive property of multiplication over addition, the Xi term would be multiplied by m and then subtracted, making option 'a' the correct choice: Y = Yi + mX.