Question

part h does the point (3, 1) lie on the line? what does this mean in terms of the science experiment?

Explanation:

To determine if the point \((3, 1)\) lies on the line, we would typically need the equation of the line (which is not provided here). However, assuming we have a line equation (for example, if the line was from a previous part of the problem, say \(y = mx + b\)), we would substitute \(x = 3\) into the equation and check if \(y = 1\) is the result.

Step 1: Recall the line equation

Suppose the line equation from the science experiment (e.g., relating two variables like time and measurement) is \(y = \frac{1}{3}x\) (a hypothetical example).

Step 2: Substitute \(x = 3\)

Substitute \(x = 3\) into the equation:
\(y = \frac{1}{3}(3) = 1\).

Since substituting \(x = 3\) gives \(y = 1\), the point \((3, 1)\) lies on the line. In terms of the science experiment, this means that when the independent variable (e.g., time, concentration) has a value of \(3\) (units of the experiment), the dependent variable (e.g., growth, reaction rate) has a value of \(1\) (units of the experiment), and this data point follows the trend/model defined by the line.

(Note: The specific interpretation depends on the context of the experiment—e.g., if \(x\) is time in hours and \(y\) is height in cm, then at \(3\) hours, the height is \(1\) cm, consistent with the experimental model.)

Answer:

To determine if \((3, 1)\) lies on the line, substitute \(x = 3\) into the line’s equation (from the experiment) and check if \(y = 1\). If it does, the point follows the experimental trend (e.g., at \(x = 3\) units, the dependent variable is \(1\) unit, matching the model).

(If the line equation is known, substitute \(x = 3\): if \(y = 1\), the point lies on the line, meaning the experiment’s data at \(x = 3\) aligns with the model.)