To find the intercepts of the graph of the equation [tex]\( -3x + 2y = 20 \)[/tex]:
### Finding the [tex]\( x \)[/tex]-Intercept:
The [tex]\( x \)[/tex]-intercept is the point where the graph crosses the [tex]\( x \)[/tex]-axis. At this point, [tex]\( y = 0 \)[/tex].
1. Set [tex]\( y = 0 \)[/tex] in the equation:
[tex]\[
-3x + 2(0) = 20
\][/tex]
Simplifying this, we have:
[tex]\[
-3x = 20
\][/tex]
2. Solve for [tex]\( x \)[/tex]:
[tex]\[
x = \frac{20}{-3} = -\frac{20}{3}
\][/tex]
Thus, the [tex]\( x \)[/tex]-intercept is [tex]\( -\frac{20}{3} \)[/tex].
### Finding the [tex]\( y \)[/tex]-Intercept:
The [tex]\( y \)[/tex]-intercept is the point where the graph crosses the [tex]\( y \)[/tex]-axis. At this point, [tex]\( x = 0 \)[/tex].
1. Set [tex]\( x = 0 \)[/tex] in the equation:
[tex]\[
-3(0) + 2y = 20
\][/tex]
Simplifying this, we have:
[tex]\[
2y = 20
\][/tex]
2. Solve for [tex]\( y \)[/tex]:
[tex]\[
y = \frac{20}{2} = 10
\][/tex]
Thus, the [tex]\( y \)[/tex]-intercept is [tex]\( 10 \)[/tex].
### Final Answers:
- The [tex]\( x \)[/tex]-intercept is [tex]\( \boxed{-\frac{20}{3}} \)[/tex].
- The [tex]\( y \)[/tex]-intercept is [tex]\( \boxed{10} \)[/tex].
