To find the [tex]\( x \)[/tex]-intercept and the [tex]\( y \)[/tex]-intercept of the graph of the equation [tex]\( 6x + 4y = 72 \)[/tex]:
Step-by-Step Solution:
1. Finding the [tex]\( x \)[/tex]-intercept:
- The [tex]\( x \)[/tex]-intercept occurs where the graph of the equation crosses the [tex]\( x \)[/tex]-axis. At this point, the value of [tex]\( y \)[/tex] is [tex]\( 0 \)[/tex].
- Substitute [tex]\( y = 0 \)[/tex] into the equation:
[tex]\[
6x + 4(0) = 72
\][/tex]
Simplify the equation:
[tex]\[
6x = 72
\][/tex]
Solve for [tex]\( x \)[/tex]:
[tex]\[
x = \frac{72}{6} = 12
\][/tex]
- Therefore, the [tex]\( x \)[/tex]-intercept is [tex]\( 12 \)[/tex].
2. Finding the [tex]\( y \)[/tex]-intercept:
- The [tex]\( y \)[/tex]-intercept occurs where the graph of the equation crosses the [tex]\( y \)[/tex]-axis. At this point, the value of [tex]\( x \)[/tex] is [tex]\( 0 \)[/tex].
- Substitute [tex]\( x = 0 \)[/tex] into the equation:
[tex]\[
6(0) + 4y = 72
\][/tex]
Simplify the equation:
[tex]\[
4y = 72
\][/tex]
Solve for [tex]\( y \)[/tex]:
[tex]\[
y = \frac{72}{4} = 18
\][/tex]
- Therefore, the [tex]\( y \)[/tex]-intercept is [tex]\( 18 \)[/tex].
In conclusion, the [tex]\( x \)[/tex]-intercept is [tex]\( 12 \)[/tex] and the [tex]\( y \)[/tex]-intercept is [tex]\( 18 \)[/tex].
To fill in the blank for the [tex]\( x \)[/tex]-intercept, we write:
The [tex]\( x \)[/tex]-intercept is [tex]\( 12 \)[/tex].
