‘Which graph represents the equation y = -1/2x – 3? A) B) C) D) ‘
The Correct Answer and Explanation is:
Correct Answer: The graph provided is the correct representation of the equation y = -1/2x – 3.
Explanation:
To determine which graph correctly represents a linear equation, we can analyze the equation’s properties in the slope-intercept form, which is y = mx + b.
In this form:
- b represents the y-intercept, which is the point where the line crosses the vertical y-axis.
- m represents the slope of the line, which describes its steepness and direction. The slope is calculated as “rise over run” (the change in y divided by the change in x).
Step 1: Analyze the given equation.
The equation is y = -1/2x – 3.
By comparing this to y = mx + b, we can identify:
- The y-intercept b is -3.
- The slope m is -1/2.
Step 2: Use the y-intercept to locate a point on the graph.
The y-intercept b = -3 tells us that the line must pass through the point on the y-axis where the y-value is -3. This corresponds to the coordinate point (0, -3). Looking at the provided graph, we can see that the purple line clearly intersects the y-axis at -3. This is our first confirmation that the graph is correct.
Step 3: Use the slope to find other points and verify the line’s direction.
The slope m = -1/2 tells us about the line’s steepness. A negative slope means the line goes downwards as we move from left to right. The value -1/2 can be interpreted as a “rise” of -1 and a “run” of 2.
Starting from our y-intercept (0, -3):
- A “rise” of -1 means we move down 1 unit (from y=-3 to y=-4).
- A “run” of 2 means we move right 2 units (from x=0 to x=2).
This leads us to a second point on the line: (2, -4). If we examine the graph, the line passes directly through this point. We can repeat this process from (2, -4) to find another point at (4, -5), which also lies on the graphed line.
Therefore, since the graph has a y-intercept at (0, -3) and a slope of -1/2, it is the correct visual representation of the equation y = -1/2x – 3.
