Answered

Determine the intercepts of the line. Do not round your answers.

[tex]\[ 8x - 5y = -11 \][/tex]

- [tex]\(x\)[/tex]-intercept: [tex]\(\square\)[/tex]
- [tex]\(y\)[/tex]-intercept: [tex]\(\square\)[/tex]



Answer :

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]