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

검증된 단계별 안내

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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주요 개념

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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.