7th Grade 2nd 6 Weeks Strength Training math worksheet featuring graphing, equations, and problem-solving exercises.

1. The graph shows a proportional relationship because it is a straight line passing through the origin (0,0). This indicates that as one variable increases, the other increases at a constant rate.

2. The slope of the line is 3. This means for every 1 unit increase in x, y increases by 3 units. The equation of the line is y = 3x.

3. The point (4, 12) lies on the line. When x = 4, y = 3 × 4 = 12, which matches the point.

4. The slope is calculated as rise over run: (6 - 0)/(2 - 0) = 6/2 = 3. This confirms the constant rate of change.

5. The graph represents a proportional relationship with a constant of proportionality of 3. The unit rate is 3, meaning y changes by 3 for every 1-unit change in x.

6. The equation y = 3x correctly models the relationship shown in the graph, as all points satisfy this equation.

7. The slope of 3 indicates the rate of change. In context, if x represents hours and y represents miles, the object moves at 3 miles per hour.

8. The graph is linear and passes through the origin, confirming a direct proportion between x and y with no initial value or offset.

9. The table values match the graph: when x=1, y=3; x=2, y=6; x=3, y=9; x=4, y=12 — all consistent with y = 3x.

10. The constant of proportionality is 3, derived from the slope of the line and verified by multiple points on the graph.