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Instructions: State the x- and y-intercepts (as coordinate points) of the linear function.

[tex]2x - y = 4[/tex]

x-Intercept: [tex]\square[/tex]

y-Intercept: [tex]\square[/tex]

Sagot :

GinnyAnsweridn
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].
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