Graph the inequality on a plane. y>5x.
I think that it should be a dashed line that should be a horizontal line but I'm not totally sure.
Could you please help me with this graph?
Thanks.
The equation of your relations become the boundary lines,
if you are dealing with < or > , draw a dotted line, since the points on the actual line are not included
if you are dealing with ≤ or ≥ then draw a solid line to show the points on the actual line are part of the relation.
so for y >5
consider y = 5, which is a horizontal line 5 units above the x-axis.
but since it is > , draw a dotted line and shade in everything above the line (above for >, below for <)
Any equation of the form y = c is a horizontal line,
any equation of the form x = c is a vertical line
To graph the inequality y > 5x, we can start by graphing the line y = 5x as a boundary line, and then determining which side of the line represents the solution to the inequality.
1. First, graph the line y = 5x. To do this, plot a few points that satisfy the equation. For example, when x = 0, y will also be 0 (0 = 5(0)). When x = 1, y will be 5 (5 = 5(1)), etc.
- Point (0, 0)
- Point (1, 5)
- Point (2, 10)
- Point (-1, -5)
2. Now connect the plotted points with a straight line. Since the inequality is y > 5x, the boundary line should be dashed, to indicate that points on the line are not included.
3. Finally, determine which side of the line represents the solution to the inequality. Since the inequality is y > 5x, the solution side will be above the line. Shade that region.
Please note that the graph does not include any specific range for x or y, so the graph will extend to infinity in all directions.
Here is an example of the graph:
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|<- Boundary Line (dashed)
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Of course! I can help you with that.
To graph the inequality y > 5x, we can start by graphing the boundary line y = 5x and then determining which side of the line satisfies the given inequality.
Let's begin by graphing the boundary line y = 5x. To do this, start by determining two points that lie on the line. One easy way to find points is by setting x to a specific value and solving for y.
Let's choose x = 0:
When x = 0, y = 5(0) = 0. So one point on the line is (0, 0).
Now let's choose another value for x, such as x = 1:
When x = 1, y = 5(1) = 5. So another point on the line is (1, 5).
Plot these two points on a coordinate plane, and draw a straight line passing through them. Make sure the line extends beyond the points in both directions.
Now, to determine which side of the line satisfies the inequality y > 5x, we can use a test point. Any point that satisfies the inequality can be used as a test point.
For simplicity, let's choose the point (0, 0) as our test point. Substitute the x and y values of the test point into the inequality, y > 5x:
0 > 5(0)
Simplifying this expression, we have:
0 > 0
Since this statement is false, the test point (0, 0) does not satisfy the inequality y > 5x. Therefore, we shade the side of the line that does not include the point (0, 0). In other words, shade the region above the line.
Finally, draw a dashed line to represent that points on the boundary line itself are not included in the solution.
I hope this helps!