To solve for the x-intercept and y-intercept of the equation [tex]\(2x - y = 4\)[/tex], let's proceed step-by-step:
### Finding the x-intercept:
The x-intercept is found by setting [tex]\(y = 0\)[/tex] in the equation and solving for [tex]\(x\)[/tex].
1. Start with the equation:
[tex]\[
2x - y = 4
\][/tex]
2. Set [tex]\(y = 0\)[/tex]:
[tex]\[
2x - 0 = 4
\][/tex]
3. Simplify the equation:
[tex]\[
2x = 4
\][/tex]
4. Solve for [tex]\(x\)[/tex]:
[tex]\[
x = \frac{4}{2} = 2
\][/tex]
So, the x-intercept is at the point [tex]\((2, 0)\)[/tex].
### Finding the y-intercept:
The y-intercept is found by setting [tex]\(x = 0\)[/tex] in the equation and solving for [tex]\(y\)[/tex].
1. Start with the equation:
[tex]\[
2x - y = 4
\][/tex]
2. Set [tex]\(x = 0\)[/tex]:
[tex]\[
2 \cdot 0 - y = 4
\][/tex]
3. Simplify the equation:
[tex]\[
- y = 4
\][/tex]
4. Solve for [tex]\(y\)[/tex]:
[tex]\[
y = -4
\][/tex]
So, the y-intercept is at the point [tex]\((0, -4)\)[/tex].
### Graphing the Line:
Now that we have the intercepts:
- The x-intercept is at [tex]\((2, 0)\)[/tex].
- The y-intercept is at [tex]\((0, -4)\)[/tex].
To graph the line, follow these steps:
1. Plot the x-intercept [tex]\((2, 0)\)[/tex] on the coordinate plane.
2. Plot the y-intercept [tex]\((0, -4)\)[/tex] on the coordinate plane.
3. Draw a straight line through these two points. This line represents the equation [tex]\(2x - y = 4\)[/tex].
By using the intercepts, you can effectively and accurately draw the graphical representation of the line.
