Final answer:
The given equations represent linear relationships between two variables, x and y. Equation 1 suggests a fixed sum of 20, Equation 2 might model a cost relationship, and Equation 3 implies a weighted relationship with four times y plus x equaling 28. They can be graphically represented by straight lines.
Step-by-step explanation:
Each of the given equations represents a linear equation in two variables, x and y. These equations can be used to model relationships between two quantities in various contexts.
- Equation 1: x + y = 20. This equation implies that the sum of the variables x and y is always 20. It can represent a scenario where the combination of two numbers or measures always adds up to a fixed total.
- Equation 2: 2.50x + y = 15. Here, the relationship between x and y is such that 2.50 times the value of x added to y equals 15. This could model a situation where, for example, x represents the number of items purchased at $2.50 each, and y represents an additional amount or charge, with a total cost of $15.
- Equation 3: x + 4y = 28. In this equation, one unit of x plus four units of y equals 28. It might represent a case where y is weighted four times more than x in the total sum of 28.
These types of equations are often represented graphically, where each equation will form a straight line on a graph, showing all the pairs (x, y) that satisfy the equation. In Practice Test 4 Solutions 12.1 Linear Equations, you might see how to create a table of values and plot these on a graph to visualize the relationships described by these linear equations.