Find the [tex]$x$[/tex]-intercept and the [tex]$y$[/tex]-intercept of the line below.

[tex]\[ -7y + 2x = -3 \][/tex]

Answer:

[tex]$x$[/tex]-intercept: [tex]$x = \square$[/tex]

[tex]$y$[/tex]-intercept: [tex]$y = \square$[/tex]



Answer :

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]