Draw the graph of the linear equation whose solutions are represented by the points having the sum of the coordinates as 10 units.
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Here, you want x+y = 10
(4,3),(-1,6)
To draw the graph of the linear equation with the sum of the coordinates as 10 units, we need to find the equation of the line first. Here's a step-by-step explanation on how to do it:
1. Let's assume that the x-coordinate is represented by the variable "x", and the y-coordinate is represented by the variable "y". Since the sum of the coordinates is 10 units, we have the equation: x + y = 10.
2. To graph this equation, we need to convert it into the slope-intercept form, which is y = mx + b. In this form, "m" represents the slope of the line and "b" represents the y-intercept.
3. Rearrange the equation x + y = 10 to get it in the slope-intercept form. Subtract x from both sides: y = -x + 10.
4. Now, we can see that the slope of the line is -1 (the coefficient of x). The y-intercept is 10 (the constant term).
5. To graph this equation, start by plotting the y-intercept, which is the point (0, 10). This is the point where the line intersects the y-axis.
6. Next, use the slope to find another point on the line. The slope of -1 means that for every 1 unit increase in x, y will decrease by 1 unit. So, starting from the y-intercept (0, 10), move 1 unit to the right and 1 unit down to get the point (1, 9).
7. Now, draw a straight line passing through the two plotted points. This line represents the graph of the linear equation x + y = 10.
Here's the graph of the linear equation x + y = 10:
```
|
10 | . (1, 9)
|
9 |
|
8 |
|
7 |
|
6 |
| .
5 |
|
4 |
|
3 |
|
2 |
|
1 |
|
-------------------
0 1 2 3 4 5
```
Note: The graph is a straight line that passes through the points (0, 10) and (1, 9).