The graph shows the number of gallons of water y in a 100...

The graph shows the number of gallons of water $y$ in a 100 -gallon tank after $x$ minutes have elapsed. (GRAPH CANNOT COPY). (a) Is water entering or leaving the tank? How much water is in the tank after 3 minutes? (b) Find the $x$ - and $y$ -intercepts. Interpret their meanings. (c) Find the slope-intercept form of the equation of the line. Interpret the slope. (d) Estimate the $x$ -coordinate of the point $(x, 50)$ that lies on the line.

The graph shows the number of gallons of water $y$ in a 100 -gallon tank after $x$ minutes have elapsed.
(GRAPH CANNOT COPY).
(a) Is water entering or leaving the tank? How much water is in the tank after 3 minutes?
(b) Find the $x$ - and $y$ -intercepts. Interpret their meanings.
(c) Find the slope-intercept form of the equation of the line. Interpret the slope.
(d) Estimate the $x$ -coordinate of the point $(x, 50)$ that lies
on the line.

Key Concepts

Graphical Interpretation

Graphical interpretation involves analyzing a visual representation of data to extract meaningful information about trends, specific values, and relationships between variables. This skill is important for understanding dynamics, such as determining values at specific times or estimating key points like intercepts from a graph.

Intercepts

Intercepts are points where the graph of a function crosses the coordinate axes. The y-intercept gives the initial value of the dependent variable when the independent variable is zero, while the x-intercept indicates the point at which the dependent variable becomes zero. Both intercepts offer essential information about the starting conditions and boundary points of the modeled scenario.

Slope (Rate of Change)

The slope of a linear function indicates the rate at which the dependent variable changes with respect to the independent variable. In applied problems, the sign and magnitude of the slope provide insight into whether a quantity is increasing or decreasing and by how much per unit of time or other measures, which is critical for understanding system dynamics.

Linear Function

A linear function represents a relationship between two variables with a constant rate of change. Its standard form, y = mx + b, simplifies the modeling of situations where one quantity changes at a constant rate relative to another, allowing for straightforward predictions and interpretations of the system's behavior.

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