Writing and Graphing Equations in Two Variables — Quiz

Question 9 • Algebra I

Which graph represents viable values for y is equal to 5 point 5 x , where x is the number of cans of tomato paste and y is the total weight of the sealed cans in ounces?

Answer

Image with description On a coordinate plane, x-axis is numbered negative 5 to positive 5 in increments of 1, and the y-axis is numbered negative 27 point 5 to 27 point 5 in increments of 5 point 5. A straight line with a positive slope begins at point (0 comma 0) and ends at point (5 comma 27 point 5)

Image with description On a coordinate plane, x-axis is numbered negative 5 to 5 in increments of 1, and the y-axis is numbered negative 27.5 to 27.5 in increments of 5.5. Solid circles appear at points (negative 5 comma negative 27.5), (negative 4 comma negative 22), negative 3 comma negative 16.5), (negative 2 comma negative 11), (negative 1 comma negative 5.5), (0 comma 0), (1 comma 5.5), (2 comma 11), (3 comma 16.5), (4 comma 22), (5 comma 27.5)

Image with description On a coordinate plane, x-axis is numbered negative 5 to 5 in increments of 1, and the y-axis is numbered negative 27.5 to 27.5 in increments of 5.5. A straight line with a positive slope begins at point (negative 5 comma negative 27 point 5) and ends at point (5 comma 27 point 5).

Image with description On a coordinate plane, x-axis is numbered negative 5 to positive 5 in increments of 1, and the y-axis is numbered negative 27.5 to 27.5 in increments of 5.5. Solid circles appear at points (0 comma 0), (1 comma 5.5), (2 comma 11), (3 comma 16.5), (4 comma 22), (5 comma 27.5)

Explanation

The relationship is y = 5.5x, so each can adds 5.5 ounces to the total weight. Since x counts cans, it must be a nonnegative whole number; the viable points include (0, 0), (1, 5.5), and (2, 11), continuing through positive whole-number values of x. Choice D shows these discrete points, while a continuous line or points for negative numbers of cans includes values that are not viable.

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