For each equation, (a) give a table with at least three ordered pairs that are solutions, and (b) graph the equation. See Examples 3 and 4. y = ½ x - 2

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Identify the given equation: $y = \frac{1}{2}x - 2$. This is a linear equation in slope-intercept form $y = mx + b$, where $m = \frac{1}{2}$ is the slope and $b = -2$ is the y-intercept.

To create a table of ordered pairs $(x, y)$, choose at least three values for $x$. For each chosen $x$, substitute it into the equation to find the corresponding $y$ value.

For example, select $x = 0$, $x = 2$, and $x = 4$. Calculate $y$ for each: - When $x=0$, $y = \frac{1}{2} \times 0 - 2 = -2$. - When $x=2$, $y = \frac{1}{2} \times 2 - 2 = 1 - 2 = -1$. - When $x=4$, $y = \frac{1}{2} \times 4 - 2 = 2 - 2 = 0$.

Organize these results into a table of ordered pairs: \[\begin{array}{c|c}$ x & y $\hline$ 0 & -2 \\ 2 & -1 \\ 4 & 0 $\end{array}\]

To graph the equation, plot the points from the table on the coordinate plane. Then, draw a straight line through these points, extending it in both directions. The slope $\frac{1}{2}$ means the line rises 1 unit for every 2 units it moves to the right.

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주요 개념

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Slope-Intercept Form of a Linear Equation

The equation y = ½ x - 2 is in slope-intercept form y = mx + b, where m is the slope and b is the y-intercept. The slope ½ indicates the line rises 1 unit for every 2 units it moves right, and the y-intercept -2 is where the line crosses the y-axis.

Finding Ordered Pairs (Solutions) for a Linear Equation

To find ordered pairs (x, y) that satisfy the equation, select values for x and compute the corresponding y values using the equation. These pairs represent points on the line and are essential for plotting the graph.

Graphing a Linear Equation

Graphing involves plotting the ordered pairs on a coordinate plane and drawing a straight line through them. The slope determines the line's angle, and the y-intercept shows where it crosses the y-axis, providing a visual representation of all solutions.