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. moisture content of snow

snow depth (in.), x	water depth (in.), f(x)
4	0.8
6	1.2
8	1.6
10	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)=0.2^x

Explanation:

Step1: Check if it's a linear relationship

Find the ratio of water depth to snow depth for each pair. For example, when $x = 2$ and $f(x)=0.4$, the ratio is $\frac{0.4}{2}=0.2$. For $x = 4$ and $f(x)=0.8$, $\frac{0.8}{4}=0.2$. Since the ratio is constant, it's a linear - relationship. The points on a graph representing the relationship will lie on a line.

Step2: Determine the equation of the relationship

The general form of a linear equation is $y = mx + b$. Since when $x = 0$ (no snow), $y = 0$ (no water), $b = 0$. And the slope $m=\frac{y}{x}=0.2$. So the function is $f(x)=0.2x$. A line through the points will pass through $(0,0)$.

Step3: Analyze each statement

• The points on a graph representing the relationship lie on a line. True, because it's a linear relationship.
• There is 0.4 inch of water to every 1 inch of snow. False, since the ratio is 0.2.
• A line through the points will pass through $(0,0)$. True, as when $x = 0$, $f(x)=0$.
• The function relating snow depth to water depth is quadratic. False, it's linear.
• The data can be represented by $f(x)=0.2x$, not $f(x)=0.2^{x}$. False.

Answer:

The points on a graph representing the relationship lie on a line; A line through the points will pass through $(0,0)$