To graph the equations y = (3/2)x - 4 and y = (-7/2)x + 6, we can plot the points and draw the lines.
For the first equation, y = (3/2)x - 4:
1. Pick arbitrary values of x and substitute them into the equation to find corresponding y-values:
- If x = 0, y = (3/2)(0) - 4 = -4.
- If x = 2, y = (3/2)(2) - 4 = 3 - 4 = -1.
- If x = -2, y = (3/2)(-2) - 4 = -3 - 4 = -7.
So, we have the points (0, -4), (2, -1), and (-2, -7).
For the second equation, y = (-7/2)x + 6:
1. Pick arbitrary values of x and substitute them into the equation to find corresponding y-values:
- If x = 0, y = (-7/2)(0) + 6 = 0 + 6 = 6.
- If x = 2, y = (-7/2)(2) + 6 = -7 + 6 = -1.
- If x = -2, y = (-7/2)(-2) + 6 = 7 + 6 = 13.
So, we have the points (0, 6), (2, -1), and (-2, 13).
Now, we can plot the points and draw the lines:
- The graph for y = (3/2)x - 4 is a straight line passing through (0, -4), (2, -1), and (-2, -7). It has a positive slope.
- The graph for y = (-7/2)x + 6 is a straight line passing through (0, 6), (2, -1), and (-2, 13). It has a negative slope.
Here is a approximate sketch of the graph:
```
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13 | o
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10 | .
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7 | .
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6 | .
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5 | .
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2 | o
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0 ---------------------
-2 -1 0 1 2
```
Please note that the accuracy may vary depending on the scale of the graph.
graph y=3/2x-4 and y=-7/2x+6
3 answers
Two points only
To graph the equations y = (3/2)x - 4 and y = (-7/2)x + 6 using only two points, we can choose any two points and plot them accordingly.
Let's choose the points (0, -4) and (2, -1) for both equations.
For y = (3/2)x - 4:
- When x = 0, y = (3/2)(0) - 4 = -4. So one point is (0, -4).
- When x = 2, y = (3/2)(2) - 4 = 3 - 4 = -1. So another point is (2, -1).
For y = (-7/2)x + 6:
- When x = 0, y = (-7/2)(0) + 6 = 0 + 6 = 6. So one point is (0, 6).
- When x = 2, y = (-7/2)(2) + 6 = -7 + 6 = -1. So another point is (2, -1).
Now, we can plot the points and draw the lines:
- The graph for y = (3/2)x - 4 is a straight line passing through (0, -4) and (2, -1), and it has a positive slope.
- The graph for y = (-7/2)x + 6 is a straight line passing through (0, 6) and (2, -1), and it has a negative slope.
Here is an approximate sketch of the graph:
```
|
6 | o
|
5 |
|
4 |
|
3 | .
|
2 | .
|
1 |
|
0 ---------------------
-2 -1 0 1 2
```
Again, please note that the accuracy may vary depending on the scale of the graph.
Let's choose the points (0, -4) and (2, -1) for both equations.
For y = (3/2)x - 4:
- When x = 0, y = (3/2)(0) - 4 = -4. So one point is (0, -4).
- When x = 2, y = (3/2)(2) - 4 = 3 - 4 = -1. So another point is (2, -1).
For y = (-7/2)x + 6:
- When x = 0, y = (-7/2)(0) + 6 = 0 + 6 = 6. So one point is (0, 6).
- When x = 2, y = (-7/2)(2) + 6 = -7 + 6 = -1. So another point is (2, -1).
Now, we can plot the points and draw the lines:
- The graph for y = (3/2)x - 4 is a straight line passing through (0, -4) and (2, -1), and it has a positive slope.
- The graph for y = (-7/2)x + 6 is a straight line passing through (0, 6) and (2, -1), and it has a negative slope.
Here is an approximate sketch of the graph:
```
|
6 | o
|
5 |
|
4 |
|
3 | .
|
2 | .
|
1 |
|
0 ---------------------
-2 -1 0 1 2
```
Again, please note that the accuracy may vary depending on the scale of the graph.
1 answer