Linear Functions — Test

Question 14 • *KCPS Algebra I (2027)

Which graph represents a function with direct variation?

Answer

Image with description A coordinate plane displays the x-axis labeled from negative 5 to 5 in increments of 1 and the y-axis labeled from negative 5 to 5 in increments of 1. A straight line with a positive slope passes through approximately the points negative 3 comma negative 4, 0 comma 1, 1 comma 2.5, and 3 comma 5.

Image with description A coordinate plane displays the x-axis labeled from negative 5 to 5 in increments of 1 and the y-axis labeled from negative 5 to 5 in increments of 1. A straight line with a negative slope passes through approximately the points negative 4 comma 5, 0 comma 1, 1 comma 0, and 5 comma negative 4.

Image with description A coordinate plane displays the x-axis labeled from negative 5 to 5 in increments of 1 and the y-axis labeled from negative 5 to 5 in increments of 1. A straight line with a negative slope passes through approximately the points negative 4 comma 2, 0 comma 0, 2 comma negative 1, and 4 comma negative 2.

Image with description A coordinate plane displays the x-axis labeled from negative 5 to 5 in increments of 1 and the y-axis labeled from negative 5 to 5 in increments of 1. A straight line with a positive slope passes through approximately the points negative 5 comma negative 3.5, 0 comma negative 2, 3 comma negative 1, and 5 comma negative 0.3.

Explanation

A direct variation has the form y = kx, so its graph is a straight line passing through the origin, (0, 0). Graph A passes through (0, 0), and its other points are consistent with a constant ratio y/x = -1/2. The other lines cross the y-axis at a value other than zero, so they do not represent direct variation.

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