distance formula = sqrt((x1 - x2)^2 + (y1 - y2)^2)
Answer:
x = 12
y = -6
distance between the x-intercept and the y-intercept is 6√5
Explanation:
To find the x-intercept, we set y = 0 and solve for x:
```
3x - 6(0) = 12 + 2x - 4(0)
3x = 12 + 2x
x = 12
```
Therefore, the x-intercept is (12, 0).
To find the y-intercept, we set x = 0 and solve for y:
```
3(0) - 6y = 12 + 2(0) - 4y
-6y = 12 - 4y
-2y = 12
y = -6
```
Therefore, the y-intercept is (0, -6).
To find the distance between the two intercepts, we can use the distance formula:
```
distance = sqrt((x1 - x2)^2 + (y1 - y2)^2)
```
In this case, (x1, y1) = (12, 0) and (x2, y2) = (0, -6), so the distance is:
```
distance = sqrt((12 - 0)^2 + (0 - (-6))^2)
distance = sqrt(144 + 36)
distance = sqrt(180)
distance = 6 * sqrt(5)
```
Therefore, the distance between the x-intercept and the y-intercept is **6√5**.
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