Questions: Graph the line with the equation y=-1/2 x-3.

Transcript text: Graph the line with the equation $y=-\frac{1}{2} x-3$.

Solution

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 = -1/2x - 3, the y-intercept is -3. This means the line crosses the y-axis at the point (0, -3).

Step 2: Identify the slope

The slope of the line is the coefficient of x, which is -1/2 in this case. This can be interpreted as a rise of -1 and a run of 2. In simpler terms for graphing: for every 2 units you move to the right along the x-axis, you should move 1 unit down along the y-axis.

Step 3: Plot the line

Start by plotting the y-intercept (0, -3) on the graph.
From the y-intercept (0,-3), move 2 units to the right and 1 unit down. This gives you a second point (2, -4).
Draw a line through both these points, extending it to the edges of the graph.

Final Answer:

The graph of the line y = -1/2x - 3 is a straight line passing through the points (0, -3) and (2, -4), and continues infinitely in both directions.

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