Question

problem 1 analyzing a graph
essential understanding you can use graphs to visually represent the
relationship between two variable quantities as they both change.
as you may have noticed in the solve it, the change in the height of the water as the
volume increases is related to the shape of the container.
got it? what are the variables in each graph? describe how the variables are
related at various points on the graph.
a. board length
b. june cell phone cost
how can you
alyze the
relationship in a
graph?

Explanation:

• For part a:
• The variables are "Time" and "Board Length".
• As time passes (x - axis), the board length (y - axis) increases in steps. This indicates that at certain intervals of time, the board length is increased by a fixed amount. For example, if we consider each horizontal segment as a period of time where the length is not changing and each vertical segment as an instant when the length is increased.
• For part b:
• The variables are "Cost" and "Minutes of Calls".
• Initially, there is a fixed cost (the vertical segment at the start). Then, as the minutes of calls (x - axis) increase, the cost (y - axis) decreases at a constant rate. This can be modeled by a linear equation of the form \(y=mx + c\), where \(m<0\) (negative slope) for the non - initial part of the graph.

Answer:

• a. Variables: Time and Board Length. Relationship: Board Length increases in steps over time.
• b. Variables: Cost and Minutes of Calls. Relationship: Initial fixed cost, then cost decreases linearly with an increase in minutes of calls.