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].
