Questions: Graph the line. y = -(3/2)x - 2

Graph the line. y = -(3/2)x - 2
Transcript text: Graph the line. \[ y=-\frac{3}{2} x-2 \]
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Solution

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Solution Steps

Step 1: Identify the y-intercept.

The y-intercept is the point where the line crosses the y-axis. In the equation y = -(3/2)x - 2, the y-intercept is -2. This gives us the point (0, -2).

Step 2: Identify the slope.

The slope of the line is represented by the coefficient of x. In this case, the slope is -3/2. This means that for every 2 units we move to the right along the x-axis, we move 3 units down along the y-axis.

Step 3: Plot the y-intercept and use the slope to find another point.

We already have the point (0, -2). Using the slope of -3/2, we can find another point. Starting at (0,-2), move 2 units to the right (x increases by 2) and 3 units down (y decreases by 3). This brings us to the point (2, -5).

Step 4: Draw the line.

Draw a straight line through the points (0, -2) and (2, -5). This line represents the graph of the equation y = -(3/2)x - 2.

Final Answer

The graph of the line is a straight line passing through the points (0, -2) and (2, -5).

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