https://file.aiquickdraw.com/mathbot/file/1721253224135cenyq2n0.png

To solve the problem and determine which of the statements is true about the graph of the equation \(5x + 4y = 1\), we'll need to find the slope and intercepts of the line. 

The given equation is in standard form \(Ax + By = C\). To find the slope and intercepts, we can convert it to slope-intercept form \(y = mx + b\), where \(m\) is the slope and \(b\) is the y-intercept.

### Step 1: Find the Slope
Convert the equation \(5x + 4y = 1\) to the slope-intercept form:

\[ 4y = -5x + 1 \]
\[ y = -\frac{5}{4}x + \frac{1}{4} \]

From this form, we can see that the slope \(m\) is \(-\frac{5}{4}\).

### Step 2: Find the y-intercept
In the slope-intercept form \(y = mx + b\), the y-intercept \(b\) is \(\frac{1}{4}\).

### Step 3: Find the x-intercept
To find the x-intercept, set \(y = 0\) in the original equation:

\[ 5x + 4(0) = 1 \]
\[ 5x = 1 \]
\[ x = \frac{1}{5} \]

### Conclusion
We can now compare these results with the given options:

- **Option A:** The graph's y-intercept is \(\frac{1}{5}\). (Incorrect, y-intercept is \(\frac{1}{4}\)).
- **Option B:** The graph's x-intercept is \(\frac{1}{4}\). (Incorrect, x-intercept is \(\frac{1}{5}\)).
- **Option C:** The graph has a slope of \(\frac{5}{4}\). (Incorrect, slope is \(-\frac{5}{4}\)).
- **Option D:** The graph has a slope of \(-\frac{4}{5}\). (Incorrect, slope is \(-\frac{5}{4}\)).

None of the options directly match the calculated values. Given these calculations:

- **Correct Slope:** \(-\frac{5}{4}\)
- **y-intercept:** \(\frac{1}{4}\)
- **x-intercept:** \(\frac{1}{5}\)

It seems there might be a typo or mistake in the provided options. If you have any more questions or need further details, please let me know.

Here are some additional questions you might find useful:
1. How do you convert an equation from standard form to slope-intercept form?
2. What is the importance of the slope in a linear equation?
3. How can you determine the x-intercept of a line from its equation?
4. What is the significance of the y-intercept in graphing linear equations?
5. How can you graph a linear equation using its slope and intercepts?

**Tip:** Always double-check your work by verifying that the calculated slope and intercepts match the given equation when converted to different forms.

Learn how to solve the linear equation 5x + 4y = 1 by finding the slope and intercepts. This problem covers key algebraic concepts, including linear equations, slope calculation, and intercept determination. Suitable for students in Grades 7-9.

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