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Find the [tex]\( x \)[/tex]-intercept and the [tex]\( y \)[/tex]-intercept of the graph of the equation.

[tex]\[ 3x + 2y = 18 \][/tex]

The [tex]\( x \)[/tex]-intercept is [tex]\(\square\)[/tex] (Type an integer.)

Sagot :

GinnyAnswer
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].
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