To determine the intercepts of the line given by the equation [tex]\( 8x - 5y = -11 \)[/tex], we need to find both the [tex]\( x \)[/tex]-intercept and the [tex]\( y \)[/tex]-intercept.
### Finding the [tex]\( x \)[/tex]-intercept:
The [tex]\( x \)[/tex]-intercept is the point where the line crosses the [tex]\( x \)[/tex]-axis. At this point, the value of [tex]\( y \)[/tex] is 0. To find the [tex]\( x \)[/tex]-intercept, set [tex]\( y = 0 \)[/tex] in the equation and solve for [tex]\( x \)[/tex]:
[tex]\[
8x - 5(0) = -11
\][/tex]
[tex]\[
8x = -11
\][/tex]
[tex]\[
x = \frac{-11}{8}
\][/tex]
So, the [tex]\( x \)[/tex]-intercept is [tex]\( \left( -\frac{11}{8}, 0 \right) \)[/tex].
### Finding the [tex]\( y \)[/tex]-intercept:
The [tex]\( y \)[/tex]-intercept is the point where the line crosses the [tex]\( y \)[/tex]-axis. At this point, the value of [tex]\( x \)[/tex] is 0. To find the [tex]\( y \)[/tex]-intercept, set [tex]\( x = 0 \)[/tex] in the equation and solve for [tex]\( y \)[/tex]:
[tex]\[
8(0) - 5y = -11
\][/tex]
[tex]\[
-5y = -11
\][/tex]
[tex]\[
y = \frac{-11}{-5}
\][/tex]
[tex]\[
y = \frac{11}{5}
\][/tex]
So, the [tex]\( y \)[/tex]-intercept is [tex]\( \left( 0, \frac{11}{5} \right) \)[/tex].
### Summary:
- The [tex]\( x \)[/tex]-intercept is [tex]\( \left( -\frac{11}{8}, 0 \right) \)[/tex].
- The [tex]\( y \)[/tex]-intercept is [tex]\( \left( 0, \frac{11}{5} \right) \)[/tex].
So, filling in the blanks:
- [tex]\( x \)[/tex]-intercept: [tex]\( -\frac{11}{8} \)[/tex], [tex]\( 0 \)[/tex]
- [tex]\( y \)[/tex]-intercept: [tex]\( 0 \)[/tex], [tex]\( \frac{11}{5} \)[/tex]
