Identify the linear equation for “ordinate is four times the abscissa” Select the equation of the line for which every point (x, y) on it satisfies y = 4 times x.

Introduction / Context:Coordinate geometry terminology: “abscissa” means x-coordinate and “ordinate” means y-coordinate. The statement says the ordinate equals four times the abscissa for every point on the line.

Given Data / Assumptions:

• Condition: y is 4 times x for all points on the line.
• We need the algebraic equation matching this condition.

Concept / Approach:Translate words to symbols: “ordinate four times the abscissa” ⇒ y = 4x. Any equivalent rearrangement is acceptable, but signs must preserve the proportionality.

Step-by-Step Solution:Start from y proportional to x with factor 4 ⇒ y = 4x.Check alternatives: y + 4x = 0 ⇒ y = −4x (wrong sign); x = 4y ⇒ y = x/4 (inverse); x + 4y = 0 ⇒ y = −x/4 (wrong sign).So the correct choice is y = 4x.

Verification / Alternative check:Test a sample point: x = 2 ⇒ y = 8. Only the option y = 4x fits.

Why Other Options Are Wrong:They represent slopes −4, 1/4, or −1/4, none of which match the stated 4.

Common Pitfalls:Confusing abscissa and ordinate or flipping 4x as x/4.

Final Answer:y = 4x