Question

graph the linear equation $y = \frac{1}{2}x - 2,$

x	y
2	-1

use the two points from the table to graph the equation.

Explanation:

Step1: Identify the first point

The first point from the table is \((0, -2)\). On the coordinate plane, this is the y - intercept. Locate the point where \(x = 0\) and \(y=-2\) (on the y - axis, 2 units below the origin).

Step2: Identify the second point

The second point from the table is \((2, -1)\). Locate the point where \(x = 2\) (2 units to the right of the origin on the x - axis) and \(y=-1\) (1 unit below the x - axis).

Step3: Draw the line

Use a straightedge to draw a line that passes through the two points \((0, -2)\) and \((2, -1)\). This line represents the graph of the linear equation \(y=\frac{1}{2}x - 2\).

(Note: Since the question is about graphing, the final answer is the graph with the line passing through \((0, -2)\) and \((2, -1)\). But as per the format, we describe the process. If we were to represent the graph, it's a straight line with slope \(\frac{1}{2}\) and y - intercept \(-2\) passing through the two given points.)

Answer:

The graph is a straight line passing through the points \((0, -2)\) and \((2, -1)\) (drawn on the given coordinate plane).