To find the intercepts of the line given by the equation [tex]\(6.2x + 8.4y + 7.2 = 0\)[/tex], we need to determine where the line crosses the [tex]\(x\)[/tex]-axis and [tex]\(y\)[/tex]-axis.
### Finding the [tex]\(x\)[/tex]-Intercept
The [tex]\(x\)[/tex]-intercept occurs where the line crosses the [tex]\(x\)[/tex]-axis. At this point, the value of [tex]\(y\)[/tex] is zero:
1. Substitute [tex]\(y = 0\)[/tex] into the equation:
[tex]\[
6.2x + 8.4(0) + 7.2 = 0
\][/tex]
2. Simplify the equation:
[tex]\[
6.2x + 7.2 = 0
\][/tex]
3. Solve for [tex]\(x\)[/tex]:
[tex]\[
6.2x = -7.2
\][/tex]
[tex]\[
x = \frac{-7.2}{6.2}
\][/tex]
4. Perform the division and round to two decimal places:
[tex]\[
x \approx -1.16
\][/tex]
The [tex]\(x\)[/tex]-intercept is [tex]\(-1.16\)[/tex].
### Finding the [tex]\(y\)[/tex]-Intercept
The [tex]\(y\)[/tex]-intercept occurs where the line crosses the [tex]\(y\)[/tex]-axis. At this point, the value of [tex]\(x\)[/tex] is zero:
1. Substitute [tex]\(x = 0\)[/tex] into the equation:
[tex]\[
6.2(0) + 8.4y + 7.2 = 0
\][/tex]
2. Simplify the equation:
[tex]\[
8.4y + 7.2 = 0
\][/tex]
3. Solve for [tex]\(y\)[/tex]:
[tex]\[
8.4y = -7.2
\][/tex]
[tex]\[
y = \frac{-7.2}{8.4}
\][/tex]
4. Perform the division and round to two decimal places:
[tex]\[
y \approx -0.86
\][/tex]
The [tex]\(y\)[/tex]-intercept is [tex]\(-0.86\)[/tex].
### Summary
(a) [tex]\(x\)[/tex]-intercept: [tex]\(-1.16\)[/tex]
(b) [tex]\(y\)[/tex]-intercept: [tex]\(-0.86\)[/tex]
