For each equation, (a) give a table with at least three ordered pairs that are solutions, and (b) graph the equation. 2x+3y=5

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Start with the given linear equation: \(2x + 3y = 5\).

To find ordered pairs \((x, y)\) that satisfy the equation, choose convenient values for \(x\) and solve for \(y\). For example, pick \(x = 0\), then solve \(2(0) + 3y = 5\) to find \(y\).

Repeat the process for at least two more values of \(x\), such as \(x = 1\) and \(x = -1\), solving for \(y\) each time to get corresponding ordered pairs.

Organize these ordered pairs into a table with columns labeled \(x\) and \(y\), listing the three pairs you found.

To graph the equation, plot each ordered pair on the coordinate plane and draw a straight line through these points, since the equation represents a linear function.

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Solving Linear Equations for One Variable

To find ordered pairs that satisfy the equation 2x + 3y = 5, you need to solve for one variable in terms of the other. For example, solving for y gives y = (5 - 2x)/3, allowing you to choose values for x and compute corresponding y values.

Ordered Pairs as Solutions to Equations

An ordered pair (x, y) is a solution to the equation if substituting x and y into the equation makes it true. Creating a table of ordered pairs involves selecting values for one variable and calculating the other, which helps visualize the relationship between x and y.

Graphing Linear Equations

Graphing the equation 2x + 3y = 5 involves plotting the ordered pairs on the coordinate plane and drawing a straight line through them. This line represents all solutions to the equation, showing the linear relationship between x and y.

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