If the point (2,3) is on the graph of an equation in x and y...

If the point $(2,3)$ is on the graph of an equation in $x$ and $y$ then the equation is satisfied when we replace $x$ by _____ and $y$ by _____. Is the point $(2,3)$ on the graph of the equation $2 y=x+1 ?$ Complete the table, and
sketch a graph.

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Key Concepts

Ordered Pairs

Ordered pairs represent locations on the coordinate plane where the first element corresponds to the x-coordinate and the second to the y-coordinate. This concept is fundamental in understanding how algebraic equations and geometric graphs are related, as each ordered pair is a potential solution to an equation if it satisfies the relation between x and y.

Substitution Method

The substitution method involves replacing the variables in an equation with specific numbers to check whether the equation holds true. This is a crucial technique for verifying whether a given point lies on the graph of the equation and for solving equations overall.

Graphing Using a Table of Values

Graphing by creating a table of values involves selecting a set of x-values, calculating their corresponding y-values from the equation, and then plotting these ordered pairs on the coordinate plane. This method helps visualize the behavior of the equation, particularly in understanding the linear or nonlinear nature of the relationship between the variables.

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