To identify the [tex]\(x\)[/tex]-intercept and [tex]\(y\)[/tex]-intercept of the line given by the equation [tex]\(2x - 5y = 20\)[/tex], we need to find the points where the line crosses the [tex]\(x\)[/tex]-axis and the [tex]\(y\)[/tex]-axis.
Finding the [tex]\(x\)[/tex]-intercept:
1. The [tex]\(x\)[/tex]-intercept is the point where the line crosses the [tex]\(x\)[/tex]-axis, which means [tex]\(y = 0\)[/tex].
2. Substitute [tex]\(y = 0\)[/tex] into the equation [tex]\(2x - 5y = 20\)[/tex]:
[tex]\[
2x - 5(0) = 20
\][/tex]
3. Simplify the equation:
[tex]\[
2x = 20
\][/tex]
4. Solve for [tex]\(x\)[/tex]:
[tex]\[
x = \frac{20}{2} = 10
\][/tex]
5. Therefore, the [tex]\(x\)[/tex]-intercept is [tex]\((10, 0)\)[/tex].
Finding the [tex]\(y\)[/tex]-intercept:
1. The [tex]\(y\)[/tex]-intercept is the point where the line crosses the [tex]\(y\)[/tex]-axis, which means [tex]\(x = 0\)[/tex].
2. Substitute [tex]\(x = 0\)[/tex] into the equation [tex]\(2x - 5y = 20\)[/tex]:
[tex]\[
2(0) - 5y = 20
\][/tex]
3. Simplify the equation:
[tex]\[
-5y = 20
\][/tex]
4. Solve for [tex]\(y\)[/tex]:
[tex]\[
y = \frac{20}{-5} = -4
\][/tex]
5. Therefore, the [tex]\(y\)[/tex]-intercept is [tex]\((0, -4)\)[/tex].
So, the correct identification of the intercepts is:
- The [tex]\(x\)[/tex]-intercept is [tex]\((10, 0)\)[/tex]
- The [tex]\(y\)[/tex]-intercept is [tex]\((0, -4)\)[/tex]
Thus, the first statement is correct:
- The [tex]\(x\)[/tex]-intercept is [tex]\((10,0)\)[/tex] and the [tex]\(y\)[/tex]-intercept is [tex]\((0,-4)\)[/tex].
