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Question 1 • Algebra I

Which graph represents a function with direct variation?

Answer

Image with description A coordinate plane has both x and y axes labeled from negative 5 to 5. A line is plotted that passes through the point negative 4 comma 2, the point 0 comma 0, and the point 4 comma negative 2.

Image with description A coordinate plane has both x and y axes labeled from negative 5 to 5. An upward-opening parabola is plotted with a vertex at the point 0 comma 0, passing through the point 2 comma 4 and the point negative 2 comma 4.

Image with description A coordinate plane has both x and y axes labeled from negative 5 to 5. A line is plotted that passes through the point negative 2 comma negative 3, the point 0 comma 1, and the point 1 comma 3.

Image with description A coordinate plane has both x and y axes labeled from negative 5 to 5. A V-shape is plotted with a vertex at the point 0 comma 0, passing through the point 2 comma 2 and the point negative 2 comma 2.

Explanation

A direct variation has the form y = kx, so its graph is a straight line passing through the origin. Choice A is a line through (0, 0); its other points also fit y = −½x. Choice C is a line but does not pass through the origin, while B and D are not straight lines.

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