Question

POSSIBLE POINTS: 7.69
The equation 4x-5y=4u is in standard form and tells us the x-intercept and y-intercept easily. What are the x and y intercepts for this equation?
Responses

The line crosses the x-axis at (4, 40) and the y-axis at (-8, 40)
The line crosses the x-axis at (4, 40) and the y-axis at (-8, 40)

The line crosses the x-axis at (10, 0) and the y-axis at (0, -8)
The line crosses the x-axis at (10, 0) and the y-axis at (0, -8)

The line crosses the x-axis at (-8, 0) and the y-axis at (0, 10)
The line crosses the x-axis at (-8, 0) and the y-axis at (0, 10)

The line crosses the x-axis at (4, 0) and the y-axis at (0, -5)
The line crosses the x-axis at (4, 0) and the y-axis at (0, -5)

The line crosses the x-axis at (0, 10) and the y-axis at (-8, 0)

Answer 1

To find the x-intercept and y-intercept of the equation \(4x - 5y = 4u\), we can set \(y = 0\) to find the x-intercept and set \(x = 0\) to find the y-intercept.

1. **Finding the x-intercept**:
Set \(y = 0\):
\[
4x - 5(0) = 4u \implies 4x = 4u \implies x = u
\]
Therefore, the x-intercept is \((u, 0)\).

2. **Finding the y-intercept**:
Set \(x = 0\):
\[
4(0) - 5y = 4u \implies -5y = 4u \implies y = -\frac{4u}{5}
\]
Therefore, the y-intercept is \((0, -\frac{4u}{5})\).

Since the exact value of \(u\) is not specified, we cannot determine the specific intercept points. However, we can look at the responses provided to see if any relate to generic values.

Examining the options:
- All proposed intercepts relate to specific values that would assign \(u\) a numeric value, so without further information on \(u\), we cannot definitively match them.

Assuming \(u = 10\), we can find intercepts:
1. X-intercept: Assuming \(u = 10\) → (10, 0)
2. Y-intercept: Known if \(u = 10\) → (0, -8)

So the correct response when \(u = 10\) is:
**The line crosses the x-axis at (10, 0) and the y-axis at (0, -8)**

This indicates the values can change based on \(u\), but with the assumed \(u = 10\), this option stands correct.