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.