Questions: Graph the line. y=1/2 x-2

Graph the line. y=1/2 x-2
Transcript text: Graph the line. \[ y=\frac{1}{2} x-2 \]
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Solution

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Solution Steps

Step 1: Find the y-intercept

The y-intercept is the value of _y_ when _x_ = 0. Plugging _x_ = 0 into the equation yields y = (1/2)(0) - 2 = -2. Therefore, the y-intercept is at the point (0,-2).

Step 2: Find the slope

The equation of the line is in slope-intercept form, y = mx + b, where m is the slope. In this case, m = 1/2.

Step 3: Plot the line using the y-intercept and slope

First, plot the y-intercept (0,-2). Since the slope is 1/2, this means that from any point on the line, you can find another point on the line by moving 1 unit up (rise) and 2 units to the right (run). Starting at the y-intercept, we move up 1 unit and right 2 units to reach the point (2,-1). Draw a line through these two points.

Final Answer: The graph is a line passing through the points (0, -2) and (2, -1).

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