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Sagot :
To find the intercepts for the equation [tex]\(-x + 3y = 6\)[/tex], follow these steps:
### Finding the [tex]\(x\)[/tex]-intercept:
To find the [tex]\(x\)[/tex]-intercept, set [tex]\(y = 0\)[/tex] and solve for [tex]\(x\)[/tex].
1. Substitute [tex]\(y = 0\)[/tex] in the equation [tex]\(-x + 3y = 6\)[/tex]:
[tex]\[ -x + 3(0) = 6 \][/tex]
2. Simplify the equation:
[tex]\[ -x = 6 \][/tex]
3. Solve for [tex]\(x\)[/tex]:
[tex]\[ x = -6 \][/tex]
So, the [tex]\(x\)[/tex]-intercept is [tex]\((-6, 0)\)[/tex].
### Finding the [tex]\(y\)[/tex]-intercept:
To find the [tex]\(y\)[/tex]-intercept, set [tex]\(x = 0\)[/tex] and solve for [tex]\(y\)[/tex].
1. Substitute [tex]\(x = 0\)[/tex] in the equation [tex]\(-x + 3y = 6\)[/tex]:
[tex]\[ -0 + 3y = 6 \][/tex]
2. Simplify the equation:
[tex]\[ 3y = 6 \][/tex]
3. Solve for [tex]\(y\)[/tex]:
[tex]\[ y = \frac{6}{3} = 2 \][/tex]
So, the [tex]\(y\)[/tex]-intercept is [tex]\((0, 2)\)[/tex].
In summary:
- The [tex]\(x\)[/tex]-intercept is [tex]\((-6, 0)\)[/tex]
- The [tex]\(y\)[/tex]-intercept is [tex]\((0, 2)\)[/tex]
### Finding the [tex]\(x\)[/tex]-intercept:
To find the [tex]\(x\)[/tex]-intercept, set [tex]\(y = 0\)[/tex] and solve for [tex]\(x\)[/tex].
1. Substitute [tex]\(y = 0\)[/tex] in the equation [tex]\(-x + 3y = 6\)[/tex]:
[tex]\[ -x + 3(0) = 6 \][/tex]
2. Simplify the equation:
[tex]\[ -x = 6 \][/tex]
3. Solve for [tex]\(x\)[/tex]:
[tex]\[ x = -6 \][/tex]
So, the [tex]\(x\)[/tex]-intercept is [tex]\((-6, 0)\)[/tex].
### Finding the [tex]\(y\)[/tex]-intercept:
To find the [tex]\(y\)[/tex]-intercept, set [tex]\(x = 0\)[/tex] and solve for [tex]\(y\)[/tex].
1. Substitute [tex]\(x = 0\)[/tex] in the equation [tex]\(-x + 3y = 6\)[/tex]:
[tex]\[ -0 + 3y = 6 \][/tex]
2. Simplify the equation:
[tex]\[ 3y = 6 \][/tex]
3. Solve for [tex]\(y\)[/tex]:
[tex]\[ y = \frac{6}{3} = 2 \][/tex]
So, the [tex]\(y\)[/tex]-intercept is [tex]\((0, 2)\)[/tex].
In summary:
- The [tex]\(x\)[/tex]-intercept is [tex]\((-6, 0)\)[/tex]
- The [tex]\(y\)[/tex]-intercept is [tex]\((0, 2)\)[/tex]
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