To find the intercepts of the given line equation [tex]\( -7x + 6y = 9 \)[/tex], we follow these steps:
### Finding the [tex]\(x\)[/tex]-Intercept
1. The [tex]\(x\)[/tex]-intercept is the point where the line crosses the [tex]\(x\)[/tex]-axis. At this point, [tex]\(y = 0\)[/tex].
2. Substitute [tex]\(y = 0\)[/tex] into the equation [tex]\( -7x + 6y = 9 \)[/tex]:
[tex]\[
-7x + 6(0) = 9
\][/tex]
3. Simplify the equation:
[tex]\[
-7x = 9
\][/tex]
4. Solve for [tex]\(x\)[/tex]:
[tex]\[
x = \frac{9}{-7}
\][/tex]
5. Simplifying the fraction:
[tex]\[
x = -1.2857142857142858
\][/tex]
So, the [tex]\(x\)[/tex]-intercept is [tex]\(-1.2857142857142858\)[/tex].
### Finding the [tex]\(y\)[/tex]-Intercept
1. The [tex]\(y\)[/tex]-intercept is the point where the line crosses the [tex]\(y\)[/tex]-axis. At this point, [tex]\(x = 0\)[/tex].
2. Substitute [tex]\(x = 0\)[/tex] into the equation [tex]\( -7x + 6y = 9 \)[/tex]:
[tex]\[
-7(0) + 6y = 9
\][/tex]
3. Simplify the equation:
[tex]\[
6y = 9
\][/tex]
4. Solve for [tex]\(y\)[/tex]:
[tex]\[
y = \frac{9}{6}
\][/tex]
5. Simplifying the fraction:
[tex]\[
y = 1.5
\][/tex]
So, the [tex]\(y\)[/tex]-intercept is [tex]\(1.5\)[/tex].
Therefore, the intercepts are:
- [tex]\(x\)[/tex]-intercept: [tex]\(-1.2857142857142858\)[/tex]
- [tex]\(y\)[/tex]-intercept: [tex]\(1.5\)[/tex]
