To determine the [tex]\(x\)[/tex]-intercept and [tex]\(y\)[/tex]-intercept for the given equation [tex]\( -6x + 3y = 18.9 \)[/tex], you need to solve the equation for each intercept separately.
### Finding the [tex]\(x\)[/tex]-intercept:
1. The [tex]\(x\)[/tex]-intercept occurs where [tex]\(y = 0\)[/tex].
2. Substitute [tex]\(y = 0\)[/tex] into the equation:
[tex]\[
-6x + 3(0) = 18.9
\][/tex]
This simplifies to:
[tex]\[
-6x = 18.9
\][/tex]
3. Solve for [tex]\(x\)[/tex]:
[tex]\[
x = \frac{18.9}{-6}
\][/tex]
4. Simplify the result:
[tex]\[
x = -3.15
\][/tex]
Thus, the [tex]\(x\)[/tex]-intercept is [tex]\(-3.15\)[/tex].
### Finding the [tex]\(y\)[/tex]-intercept:
1. The [tex]\(y\)[/tex]-intercept occurs where [tex]\(x = 0\)[/tex].
2. Substitute [tex]\(x = 0\)[/tex] into the equation:
[tex]\[
-6(0) + 3y = 18.9
\][/tex]
This simplifies to:
[tex]\[
3y = 18.9
\][/tex]
3. Solve for [tex]\(y\)[/tex]:
[tex]\[
y = \frac{18.9}{3}
\][/tex]
4. Simplify the result:
[tex]\[
y = 6.3
\][/tex]
Thus, the [tex]\(y\)[/tex]-intercept is [tex]\(6.3\)[/tex].
### Final answers:
[tex]\[
x\text{-intercept} = -3.15
\][/tex]
[tex]\[
y\text{-intercept} = 6.3
\][/tex]
