yintercept is (0,6) and is < or > (5,1) find a graph
To determine whether the y-intercept (0, 6) is greater than or less than the point (5, 1), we need to compare the y-coordinate values.
Given that the y-coordinate of the y-intercept is 6, and the y-coordinate of the other point is 1, we can see that 6 is greater than 1.
Therefore, the y-intercept (0, 6) is greater than the point (5, 1).
Now let's draw a graph to represent this information:
First, plot the y-intercept (0, 6) on the y-axis at 6 units:
|
6 | ●
|________________
0 5
Next, plot the other point (5, 1) on the graph at 5 units on the x-axis and 1 unit on the y-axis:
|
6 | ●
5 | ●
|________________
0 5
Draw a line connecting the two points:
|
6 | ●
5 |───────────────●
|________________
0 5
This line represents the linear equation that connects the y-intercept (0, 6) with the point (5, 1).
To graph the inequality, we need to plot the points on a coordinate plane and draw a line passing through them.
1. Start by plotting the y-intercept, (0,6). This means that the line crosses the y-axis at y = 6. Mark this point on the graph.
2. The inequality states that the line is either greater than or less than the point (5,1). To determine which, we can substitute (5,1) into the inequality and check the result.
If the result is true, the line should be drawn above the point (5,1).
If the result is false, the line should be drawn below the point (5,1).
3. Now, let's substitute the coordinates of (5,1) into the inequality. If the inequality is true, the line will be above (5,1); if it's false, the line will be below (5,1).
Let's assume the inequality is "greater than" (>):
Substitute the x-coordinate (5) and y-coordinate (1) into the inequality:
6 > 1
Since 6 is indeed greater than 1, the line should be drawn above (5,1).
4. Draw a straight line passing through the y-intercept (0,6) and above the point (5,1). This line represents the region of the graph that satisfies the inequality.
Here is the graph of the inequality y > x + 6:
```
^
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| .
| .
| .
| . .
| . .
| . .
|______________________________>
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| |
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0 5
```
The shaded area above the line represents the solution to the inequality y > x + 6. Any point located in the shaded region will satisfy the inequality.
To find the graph for the given information, we need to compare the y-intercept (0,6) and the point (5,1) to determine whether the y-intercept is greater or less than the other point.
When comparing two points, we need to consider their y-coordinates since we are interested in determining the relationship on the y-axis.
Given that the y-intercept is (0,6), we know that the y-coordinate is 6 at x=0. And for the point (5,1), the y-coordinate is 1 at x=5.
To determine whether the y-intercept is greater or less than the point (5,1), we compare the y-coordinates. In our case, 6 is greater than 1. So we can say that the y-intercept (0,6) is greater than the point (5,1).
To graph this, we simply plot the two points on a coordinate plane and draw a line passing through them.
The graph would look something like this:
| *
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|
|
_____|_____________
0 5
The point (0,6) would be plotted higher on the y-axis than the point (5,1), showing that the y-intercept is greater. The line passing through the two points would depict the relationship between them.
Note: The instructions provided in the question ("is < or >") might imply a comparison operator. However, since we are dealing with points, we cannot determine if one point is greater or lesser than another, only their respective y-coordinates.