To find the intercepts of the equation [tex]\(3x + 2y = 18\)[/tex], follow these steps:
1. Finding the [tex]\(x\)[/tex]-intercept:
- To find the [tex]\(x\)[/tex]-intercept, we set [tex]\(y = 0\)[/tex] and solve for [tex]\(x\)[/tex].
- Plugging in [tex]\(y = 0\)[/tex] into the equation [tex]\(3x + 2y = 18\)[/tex] gives:
[tex]\[
3x + 2(0) = 18
\][/tex]
[tex]\[
3x = 18
\][/tex]
[tex]\[
x = \frac{18}{3}
\][/tex]
[tex]\[
x = 6
\][/tex]
- Therefore, the [tex]\(x\)[/tex]-intercept is [tex]\(6\)[/tex].
2. Finding the [tex]\(y\)[/tex]-intercept:
- To find the [tex]\(y\)[/tex]-intercept, we set [tex]\(x = 0\)[/tex] and solve for [tex]\(y\)[/tex].
- Plugging in [tex]\(x = 0\)[/tex] into the equation [tex]\(3x + 2y = 18\)[/tex] gives:
[tex]\[
3(0) + 2y = 18
\][/tex]
[tex]\[
2y = 18
\][/tex]
[tex]\[
y = \frac{18}{2}
\][/tex]
[tex]\[
y = 9
\][/tex]
- Therefore, the [tex]\(y\)[/tex]-intercept is [tex]\(9\)[/tex].
Hence, the [tex]\(x\)[/tex]-intercept is [tex]\(6\)[/tex].
