Which graph represents the linier function y= 1/3x - 4
There is no graph provided, so I cannot provide an answer with a visual representation. However, I can explain how to graph the linear function y = 1/3x - 4:
1. Find the y-intercept: This is the point where the line crosses the y-axis. In this case, the y-intercept is -4, since the constant term in the equation is -4.
2. Find another point on the line: To graph a line, you need at least two points. You can choose any x-value for this second point, but it's usually easiest to choose an x-value that is a multiple of the denominator of the slope (in this case, 3). So, if you choose x = 3, then y = 1/3(3) - 4 = -3.
3. Plot the two points: The y-intercept is at (0,-4) and the other point you found is at (3,-3).
4. Draw the line through the two points: This is the graph of the linear function y = 1/3x - 4.
The linear function y = (1/3)x - 4 represents a line on a graph. To draw the graph, follow these steps:
1. Plot the y-intercept: The y-intercept is the point where the line crosses the y-axis when x = 0. In this case, the y-intercept is -4. Mark the point (0, -4) on the graph.
2. Determine the slope: The slope of the line is represented by the coefficient of x, which is 1/3. The slope determines how steep the line is.
3. Use the slope to find additional points: To find additional points on the line, you can use the slope. Move vertically up or down by 1 unit and horizontally right or left by 3 units (or vice versa) to find the next point.
- Starting from the y-intercept (0, -4), go up 1 unit and right 3 units to (3, -3).
- From (3, -3), go up 1 unit and right 3 units to (6, -2).
- Repeat this process to find more points if desired.
4. Connect the points: Once you have a few points plotted, draw a straight line through them. The line should extend infinitely in both directions.
The graph of the linear function y = (1/3)x - 4 would look like this:
| .
-2 | .
| .
-4 | .
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-6 -3 0 3 6
x-axis