Proportion Graphs

Question 1

A rain gauge records that each minute of rain adds exactly 2 mm of water to a garden plot, so the amount of water collected (y) is directly proportional to the number of minutes of rain (x). Which statement correctly explains why the graph of this relationship must contain the point (0, 0)?

Accepted Answer

Because when x = 0 minutes of rain, no water is added, so y = 0 mm; the equation y = 2x gives y = 0 when x = 0, so (0, 0) lies on the line.

Answer

Because any line with a slope of 2 automatically passes through the origin, regardless of its equation.

Answer

Because the double number lines used for the graph both start at zero, the plotted line is forced to begin at (0, 0).

Answer

Because the constant of proportionality (2) is multiplied by the x‑value, and multiplying any number by 2 always yields a point on the origin.

Question 2

Why does the graph of a directly proportional relationship always pass through the point (0, 0)?

Accepted Answer

Because when one quantity is zero, the other quantity must also be zero.

Answer

Because the line always has a slope of 1.

Answer

Because the graph is a vertical line.

Answer

Because the y‑intercept is always 5.

Question 3

A student draws a line through the origin (0,0) that also passes through the points (2,5) and (4,10). Which of the following points would also lie on that same line?

Accepted Answer

(6,15)

Answer

(6,12)

Answer

(8,17)

Answer

(10,24)

Try three questions

A rain gauge records that each minute of rain adds exactly 2 mm of water to a garden plot, so the amount of water collected (y) is directly proportional to the number of minutes of rain (x). Which statement correctly explains why the graph of this relationship must contain the point (0, 0)?

Why does the graph of a directly proportional relationship always pass through the point (0, 0)?

A student draws a line through the origin (0,0) that also passes through the points (2,5) and (4,10). Which of the following points would also lie on that same line?

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