Get expert advice and community support for all your questions on IDNLearn.com. Ask your questions and receive detailed and reliable answers from our experienced and knowledgeable community members.
Sagot :
To determine the intercepts of the linear equation [tex]\(2x - y = 4\)[/tex], we will follow these steps:
### Finding the [tex]\(x\)[/tex]-Intercept
1. To find the [tex]\(x\)[/tex]-intercept, we set [tex]\(y = 0\)[/tex] in the equation.
2. Substitute [tex]\(y = 0\)[/tex] into [tex]\(2x - y = 4\)[/tex]:
[tex]\[ 2x - 0 = 4 \][/tex]
3. Simplify the equation:
[tex]\[ 2x = 4 \][/tex]
4. Solve for [tex]\(x\)[/tex] by dividing both sides by 2:
[tex]\[ x = \frac{4}{2} = 2 \][/tex]
5. Therefore, the [tex]\(x\)[/tex]-intercept is at the point [tex]\( (2, 0) \)[/tex].
### Finding the [tex]\(y\)[/tex]-Intercept
1. To find the [tex]\(y\)[/tex]-intercept, we set [tex]\(x = 0\)[/tex] in the equation.
2. Substitute [tex]\(x = 0\)[/tex] into [tex]\(2x - y = 4\)[/tex]:
[tex]\[ 2 \cdot 0 - y = 4 \][/tex]
3. Simplify the equation:
[tex]\[ -y = 4 \][/tex]
4. Solve for [tex]\(y\)[/tex] by multiplying both sides by [tex]\(-1\)[/tex]:
[tex]\[ y = -4 \][/tex]
5. Therefore, the [tex]\(y\)[/tex]-intercept is at the point [tex]\( (0, -4) \)[/tex].
In summary:
- The [tex]\(x\)[/tex]-intercept is [tex]\((2, 0)\)[/tex].
- The [tex]\(y\)[/tex]-intercept is [tex]\((0, -4)\)[/tex].
### Finding the [tex]\(x\)[/tex]-Intercept
1. To find the [tex]\(x\)[/tex]-intercept, we set [tex]\(y = 0\)[/tex] in the equation.
2. Substitute [tex]\(y = 0\)[/tex] into [tex]\(2x - y = 4\)[/tex]:
[tex]\[ 2x - 0 = 4 \][/tex]
3. Simplify the equation:
[tex]\[ 2x = 4 \][/tex]
4. Solve for [tex]\(x\)[/tex] by dividing both sides by 2:
[tex]\[ x = \frac{4}{2} = 2 \][/tex]
5. Therefore, the [tex]\(x\)[/tex]-intercept is at the point [tex]\( (2, 0) \)[/tex].
### Finding the [tex]\(y\)[/tex]-Intercept
1. To find the [tex]\(y\)[/tex]-intercept, we set [tex]\(x = 0\)[/tex] in the equation.
2. Substitute [tex]\(x = 0\)[/tex] into [tex]\(2x - y = 4\)[/tex]:
[tex]\[ 2 \cdot 0 - y = 4 \][/tex]
3. Simplify the equation:
[tex]\[ -y = 4 \][/tex]
4. Solve for [tex]\(y\)[/tex] by multiplying both sides by [tex]\(-1\)[/tex]:
[tex]\[ y = -4 \][/tex]
5. Therefore, the [tex]\(y\)[/tex]-intercept is at the point [tex]\( (0, -4) \)[/tex].
In summary:
- The [tex]\(x\)[/tex]-intercept is [tex]\((2, 0)\)[/tex].
- The [tex]\(y\)[/tex]-intercept is [tex]\((0, -4)\)[/tex].
We appreciate every question and answer you provide. Keep engaging and finding the best solutions. This community is the perfect place to learn and grow together. Your questions deserve reliable answers. Thanks for visiting IDNLearn.com, and see you again soon for more helpful information.