To find the [tex]\(x\)[/tex] and [tex]\(y\)[/tex] intercepts for the equation [tex]\(y = -6x + 3\)[/tex], follow these steps:
### 1. Finding the [tex]\(x\)[/tex]-intercept:
The [tex]\(x\)[/tex]-intercept occurs where [tex]\(y = 0\)[/tex].
1. Set [tex]\(y\)[/tex] to 0 in the equation [tex]\(y = -6x + 3\)[/tex]:
[tex]\[
0 = -6x + 3
\][/tex]
2. Solve for [tex]\(x\)[/tex]:
[tex]\[
6x = 3
\][/tex]
[tex]\[
x = \frac{3}{6} = \frac{1}{2}
\][/tex]
3. Therefore, the [tex]\(x\)[/tex]-intercept is [tex]\(\left(\frac{1}{2}, 0\right)\)[/tex].
### 2. Finding the [tex]\(y\)[/tex]-intercept:
The [tex]\(y\)[/tex]-intercept occurs where [tex]\(x = 0\)[/tex].
1. Set [tex]\(x\)[/tex] to 0 in the equation [tex]\(y = -6x + 3\)[/tex]:
[tex]\[
y = -6(0) + 3
\][/tex]
2. Solve for [tex]\(y\)[/tex]:
[tex]\[
y = 3
\][/tex]
3. Therefore, the [tex]\(y\)[/tex]-intercept is [tex]\((0, 3)\)[/tex].
### Final Answer:
The intercepts for the equation [tex]\(y = -6x + 3\)[/tex] are:
- [tex]\(x\)[/tex]-intercept: [tex]\(\left(\frac{1}{2}, 0\right)\)[/tex]
- [tex]\(y\)[/tex]-intercept: [tex]\((0, 3)\)[/tex]
So the correct option is:
- [tex]\(\left(\frac{1}{2}, 0\right)\)[/tex] and [tex]\((0, 3)\)[/tex]
