Question

1. based on the best - fit line equation shown in your digital graph, what is the slope of your line? based on the slope from the digital graph, make corrections to your paper analysis questions number 1, if necessary.

the slope of my line is 0.289

1. which option below is the best match for your weight vs. mass graph? based on the information in the table, make corrections to your paper analysis question number 2.

	option 1	option 2	option 3

| graph | \\(\

$$\begin{tikzpicture}\ \\draw-> (0,0) -- (4,0) noderight {$x$};\ \\draw-> (0,0) -- (0,4) nodeabove {$y$};\ \\draw (0,2) -- (4,2);\ \\end{tikzpicture}$$

\\) | \\(\

$$\begin{tikzpicture}\ \\draw-> (0,0) -- (4,0) noderight {$x$};\ \\draw-> (0,0) -- (0,4) nodeabove {$y$};\ \\draw (0,0) -- (4,4);\ \\end{tikzpicture}$$

\\) | \\(\

$$\begin{tikzpicture}\ \\draw-> (0,0) -- (4,0) noderight {$x$};\ \\draw-> (0,0) -- (0,4) nodeabove {$y$};\ \\draw (0,4) toout=0,in=90 (4,0);\ \\end{tikzpicture}$$

\\) |

name of relationship	no relationship (independent)	directly proportional	inversely proportional
description of graph	horizontal line	increasing/going up	decreasing/going down
written relationship	as mass increases, weight remains the same.	as mass increases, weight increases.	as mass increases, weight decreases.

Explanation:

To determine the best - match graph for weight vs. mass, we know from physics that weight ($W$) and mass ($m$) are related by the formula $W = mg$ (where $g$ is the acceleration due to gravity, a constant). This means that weight is directly proportional to mass. A directly proportional relationship is represented by a straight - line graph that passes through the origin and has a positive slope (the graph is increasing).

• Option 1 shows a horizontal line, which represents no relationship between mass and weight (weight remains constant as mass changes), so it is incorrect.
• Option 2 shows a straight - line graph that goes up from the origin, which is characteristic of a directly proportional relationship (as mass increases, weight increases), so it is correct.
• Option 3 shows a curve that is decreasing, which represents an inversely proportional relationship (as mass increases, weight decreases), so it is incorrect.

Answer:

B. Option 2 (where the graph is a straight line going up from the origin, the relationship is "Directly Proportional", the description of the graph is "Increasing/Going Up", and the written relationship is "As mass increases, weight increases")