Identify the linear equation of a line where each point has ordinate four times its abscissa: Choose the equation whose graph satisfies y = 4 * x for all points.

Introduction / Context:This concept check asks you to match a verbal line description to its algebraic form. “Ordinate” means y-coordinate and “abscissa” means x-coordinate. Saying “the ordinate is four times the abscissa” translates directly to y = 4x for every point on the line.

Given Data / Assumptions:

• For all points (x, y) on the line: y is four times x.
• We seek the linear equation that encodes this relationship exactly.

Concept / Approach:Translate words to symbols. “y is four times x” → y = 4x. Check each option by rearranging to an explicit y = mx form where possible, and compare the slope and proportionality to 4.

Step-by-Step Solution:

Verification / Alternative check:Pick x = 2. Then y must be 8. Only y = 4x passes the test exactly for all x.

Why Other Options Are Wrong:They represent lines with slopes −4, 1/4, or −1/4, none of which encode y being four times x.

Common Pitfalls:Confusing “four times” (multiply by 4) with “one fourth” (divide by 4), or missing the negative sign when moving terms across the equals sign.

Final Answer:y = 4x