For each equation, (a) give a table with at least three ordered pairs that are solutions, and (b) graph the equation. y=(1/2)x-2

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Identify the given linear equation: \(y=\frac{1}{2}x - 2\).

To create a table of ordered pairs, choose at least three different values for \(x\). For each chosen \(x\) value, substitute it into the equation to find the corresponding \(y\) value using \(y=\frac{1}{2}x - 2\).

Calculate \(y\) for each \(x\) value: for example, if \(x=0\), then \(y=\frac{1}{2}(0) - 2\); if \(x=2\), then \(y=\frac{1}{2}(2) - 2\); if \(x=4\), then \(y=\frac{1}{2}(4) - 2\). This will give you three ordered pairs \((x, y)\).

Organize these ordered pairs into a table with two columns labeled \(x\) and \(y\), listing each pair as a row.

To graph the equation, plot each ordered pair on the coordinate plane, then draw a straight line through the points, extending it in both directions to represent all solutions of the linear equation.

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Key Concepts

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

Slope-Intercept Form of a Linear Equation

The slope-intercept form is y = mx + b, where m represents the slope and b the y-intercept. It describes a straight line on the coordinate plane, showing how y changes with x. In the given equation y = (1/2)x - 2, the slope is 1/2 and the y-intercept is -2.

Finding Ordered Pairs (Solutions) for a Linear Equation

To find ordered pairs that satisfy the equation, choose values for x and calculate the corresponding y values using the equation. Each pair (x, y) represents a point on the line. For example, if x = 0, y = (1/2)(0) - 2 = -2, so (0, -2) is a solution.

Graphing Linear Equations

Graphing involves plotting ordered pairs on the coordinate plane and connecting them to form a line. The slope indicates the line's steepness and direction, while the y-intercept shows where the line crosses the y-axis. Using at least three points ensures accuracy in the graph.

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