To find the intercepts for the given line equation [tex]\(-7y + 2x = -3\)[/tex], let's go through the solution step-by-step.
### Finding the [tex]\(x\)[/tex]-intercept:
The [tex]\(x\)[/tex]-intercept occurs where the line crosses the [tex]\(x\)[/tex]-axis. At the [tex]\(x\)[/tex]-intercept, [tex]\(y = 0\)[/tex].
1. Start with the original equation:
[tex]\[
-7y + 2x = -3
\][/tex]
2. Set [tex]\(y = 0\)[/tex]:
[tex]\[
-7(0) + 2x = -3
\][/tex]
3. Simplify the equation:
[tex]\[
2x = -3
\][/tex]
4. Solve for [tex]\(x\)[/tex]:
[tex]\[
x = \frac{-3}{2}
\][/tex]
5. Therefore, the [tex]\(x\)[/tex]-intercept is:
[tex]\[
x = -1.5
\][/tex]
### Finding the [tex]\(y\)[/tex]-intercept:
The [tex]\(y\)[/tex]-intercept occurs where the line crosses the [tex]\(y\)[/tex]-axis. At the [tex]\(y\)[/tex]-intercept, [tex]\(x = 0\)[/tex].
1. Start with the original equation:
[tex]\[
-7y + 2x = -3
\][/tex]
2. Set [tex]\(x = 0\)[/tex]:
[tex]\[
-7y + 2(0) = -3
\][/tex]
3. Simplify the equation:
[tex]\[
-7y = -3
\][/tex]
4. Solve for [tex]\(y\)[/tex]:
[tex]\[
y = \frac{-3}{-7}
\][/tex]
[tex]\[
y = \frac{3}{7}
\][/tex]
5. Therefore, the [tex]\(y\)[/tex]-intercept is:
[tex]\[
y \approx 0.42857142857142855
\][/tex]
### Summary:
- [tex]\(x\)[/tex]-intercept: [tex]\(x = -1.5\)[/tex]
- [tex]\(y\)[/tex]-intercept: [tex]\(y \approx 0.42857142857142855\)[/tex]
So, the intercepts for the line [tex]\(-7y + 2x = -3\)[/tex] are:
[tex]\[
\text{$x$-intercept: } x = -1.5
\][/tex]
[tex]\[
\text{$y$-intercept: } y \approx 0.42857142857142855
\][/tex]
