Answer:
To graph the inequality y>3x−8, you can follow these steps:
1. Start with a grid or graph paper. Label the x-axis and y-axis.
2. Identify the y-intercept: To find the y-intercept, set x = 0 and solve for y:
y=3(0)−8
y=−8
So, the y-intercept is at point (0, -8).
3. Identify the slope: The slope of the line is the coefficient of x, which is 3 in this case.
4. Plot the y-intercept: Mark the point (0, -8) on your graph
5. Use the slope to find additional points: Since the slope is 3, it means that for every 1 unit you move to the right along the x-axis, you should move 3 units up along the y-axis. Similarly, for every 1 unit you move to the left along the x-axis, you should move 3 units down along the y-axis. Plot a few more points based on this slope.
If you move 1 unit to the right from (0, -8), you arrive at (1, -5).
If you move 1 unit to the left from (0, -8), you arrive at (-1, -11).
6. Draw a dashed line: Since the inequality is y> 3x-8, the line representing the boundary should be dashed. This indicates that the points on the line are not included in the solution.
7. Shade the region above the line: Since the inequality is y>3x-8, you want to shade the area above the dashed line. This means all the points in that shaded region satisfy the inequality.
Your graph should now show a dashed line with a shaded region above it, indicating the solution to the inequality y>3x -8