UpStudy Free Solution:

To determine which graph correctly represents the equation \(V = 4 + 2t\), where \(V\) is the total volume of water and \(t\) is the elapsed time in minutes, let's analyze the equation:

1. Slope: The coefficient of \(t\) is 2, indicating a slope of 2. This means for every 1 minute increase in time, the volume increases by 2 units.

2. Y-intercept: The constant term is 4, indicating that the volume of water at \(t = 0\) is 4 units.

Now, let's check the graphs:

 The first graph shows a straight line with a positive slope and a y-intercept at \(V = 4\).

 The second graph shows discrete points.

Given that the equation \(V = 4 + 2t\) represents a continuous linear relationship, the correct graph should be a continuous straight line starting at \(V = 4\) when \(t = 0\) and increasing by 2 units for each 1 minute increase in \(t\).

Therefore, the first graph correctly represents the equation \(V = 4 + 2t\).

Supplemental Knowledge

A linear equation of the form \(V = 4 + 2t\) represents a straight line when plotted on a graph. Here, \(V\) is the dependent variable (total volume of water), and \(t\) is the independent variable (elapsed time in minutes).

 Slope (Rate of Change): The coefficient of \(t\) is 2, indicating that for each minute that passes, the volume increases by 2 units.

 Y-intercept: The constant term is 4, meaning that at \(t = 0\), the volume starts at 4 units.

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