Question

Kate packs snow into 5 identical jars. Each jar represents a different depth of snow. Kate then lets the snow in each jar completely melt. The table shows the height of the liquid in each jar as it relates to the original depth of snow in the jar.

A 2-column table with 5 rows. The first column is labeled snow depth (inches), x with entries 2, 4, 6, 8, 10. The second column is labeled water depth (inches), f(x) with entries 0.4, 0.8, 1.2, 1.6, 2.0.

Which statements are true about the relationship between the depth of the snow and the height of water in the jar after the snow is melted? Select two options.

The points on a graph representing the relationship lie on a line.
There is 0.4 inch of water to every 1 inch of snow.
A line through the points will pass through (0, 0).
The function relating snow depth to water depth is quadratic.
The data can be represented by f(x) = 0.2x.

Answer 1

Correct choices:
- The points on a graph representing the relationship lie on a line.
- The data can be represented by f(x) = 0.2x.

Reason: f(x)/x = 0.4/2 = 0.8/4 = 1.2/6 = 0.2, so the ratio is constant and the relationship is linear with slope 0.2. Therefore f(x)=0.2x (which also implies the line passes through (0,0)). The other statements are false.