Discover a world of knowledge and get your questions answered at IDNLearn.com. Find the information you need quickly and easily with our reliable and thorough Q&A platform.
Sagot :
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].
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].
Thank you for using this platform to share and learn. Keep asking and answering. We appreciate every contribution you make. Your questions deserve precise answers. Thank you for visiting IDNLearn.com, and see you again soon for more helpful information.