To determine the properties of the graph of the equation [tex]\(5x + 4y = 1\)[/tex], let's find the x-intercept and y-intercept.
1. Finding the x-intercept:
- The x-intercept occurs where the graph intersects the x-axis, which means [tex]\(y = 0\)[/tex].
- Substitute [tex]\(y = 0\)[/tex] into the equation [tex]\(5x + 4y = 1\)[/tex].
- [tex]\(5x + 4(0) = 1\)[/tex].
- [tex]\(5x = 1\)[/tex].
- Solving for [tex]\(x\)[/tex], we get [tex]\(x = \frac{1}{5}\)[/tex].
- Therefore, the x-intercept is [tex]\(0.2\)[/tex].
2. Finding the y-intercept:
- The y-intercept occurs where the graph intersects the y-axis, which means [tex]\(x = 0\)[/tex].
- Substitute [tex]\(x = 0\)[/tex] into the equation [tex]\(5x + 4y = 1\)[/tex].
- [tex]\(5(0) + 4y = 1\)[/tex].
- [tex]\(4y = 1\)[/tex].
- Solving for [tex]\(y\)[/tex], we get [tex]\(y = \frac{1}{4}\)[/tex].
- Therefore, the y-intercept is [tex]\(0.25\)[/tex].
Given these results, the graph of the equation [tex]\(5x + 4y = 1\)[/tex] has an x-intercept of [tex]\( \left( 0.2, 0 \right) \)[/tex] and a y-intercept of [tex]\( \left( 0, 0.25 \right) \)[/tex].
Now, taking into consideration the obtained x-intercept and y-intercept values, look at the answer choices and select the one which correctly reflects these intercepts. Based on the x-intercept and y-intercept, one true statement about the graph would be:
- The correct statement about the graph is that it intersects the x-axis at [tex]\( (0.2, 0) \)[/tex] and the y-axis at [tex]\( (0, 0.25) \)[/tex].
