Graph the linear function.
y equals negative 3 x plus 8
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Part 1
Use the graphing tool to graph the linear equation.
As an AI text-based platform, I am unable to directly provide a graphic image, but I can guide you through the process of graphing the linear equation \( y = -3x + 8 \) on a coordinate plane.
Here are the steps to graph this equation manually:
1. Create a coordinate plane (a graph with a horizontal x-axis and a vertical y-axis).
2. Identify the y-intercept from the equation. The y-intercept is the value where the line crosses the y-axis (where x = 0). For this equation, the y-intercept is 8. So, you would put a point on the graph at (0, 8).
3. Use the slope to identify another point. The slope of the line is -3, which means that for every 1 unit you move to the right along the x-axis, you move 3 units down on the y-axis. Since the slope is negative, you could also move 1 unit to the left and 3 units up.
4. Based on the slope, from the y-intercept (0, 8), you can move 1 unit to the right on the x-axis to (1, 8 - 3) which is (1, 5). Put a point at (1, 5) on the graph.
5. Alternatively, you can move 1 unit to the left (to -1 on the x-axis) and 3 units up to (0 + 3) which is 11 on the y-axis, giving you the point (-1, 11). Put a point at (-1, 11) on the graph.
6. Lastly, draw a straight line through the points you have plotted. The line you draw will represent the linear equation \( y = -3x + 8 \). It will continue infinitely in both directions, extending beyond the points you've plotted.
The line should look like it is leaning forward from the top left to the bottom right because of the negative slope, crossing the y-axis at y=8.
Remember, you can always plot more points if you need by continuing to apply the slope to find new points that satisfy the equation and help you draw a more accurate line.
If you're using a graphing calculator or tool, input the equation \( y = -3x + 8 \), and the tool should be able to graph the function for you.