trying to graph 2x-5y=8 and 5<2x-8 and then trying to find out what the difference is between them
The equation 2x-5y=8 is a line y=2/5 x - 8/5.
If you look at y<2/5 x - 8/5, that is below the line.
2/5x - 8/8
To graph the equation 2x-5y=8, you can follow these steps:
Step 1: Convert the equation to slope-intercept form (y = mx + b) by solving for y:
2x - 5y = 8
-5y = -2x + 8
y = (2/5)x - (8/5)
Step 2: Plot two points on the graph using the slope-intercept form. You can choose any values of x and solve for y. For example, when x = 0, y = -8/5, and when x = 5, y = 6/5.
Step 3: Draw a straight line through the two points to represent the equation. Make sure the line extends beyond the plotted points.
Next, let's analyze the inequality 5 < 2x - 8:
Step 1: Add 8 to both sides of the inequality:
5 + 8 < 2x - 8 + 8
13 < 2x
Step 2: Divide both sides of the inequality by 2:
13/2 < x
This means that x is greater than 13/2, or x > 6.5.
Now, we can compare the equation 2x - 5y = 8 and the inequality 5 < 2x - 8:
The equation represents a line on the graph, while the inequality represents the area below that line. The difference between them is that the equation 2x - 5y = 8 includes the actual line, while the inequality 5 < 2x - 8 does not include the line itself but only the region below it. This is because the inequality is strictly less than, indicated by the "<" symbol, while the equation represents an equality.