Answer :
To write an equation in standard form and find the [tex]\( x \)[/tex]- and [tex]\( y \)[/tex]-intercepts for the given line, let's consider the standard form of a linear equation: [tex]\( Ax + By = C \)[/tex].
The provided equation is: [tex]\( 4x - 5y = -1 \)[/tex].
### Finding the [tex]\( x \)[/tex]-intercept
To find the [tex]\( x \)[/tex]-intercept, set [tex]\( y = 0 \)[/tex]:
[tex]\[ 4x - 5(0) = -1 \][/tex]
[tex]\[ 4x = -1 \][/tex]
[tex]\[ x = \frac{-1}{4} \][/tex]
So, the [tex]\( x \)[/tex]-intercept is [tex]\(\left( \frac{-1}{4}, 0 \right)\)[/tex].
### Finding the [tex]\( y \)[/tex]-intercept
To find the [tex]\( y \)[/tex]-intercept, set [tex]\( x = 0 \)[/tex]:
[tex]\[ 4(0) - 5y = -1 \][/tex]
[tex]\[ -5y = -1 \][/tex]
[tex]\[ y = \frac{-1}{-5} \][/tex]
[tex]\[ y = \frac{1}{5} \][/tex]
So, the [tex]\( y \)[/tex]-intercept is [tex]\(\left( 0, \frac{1}{5} \right)\)[/tex].
### Summary:
- The equation of the line is [tex]\( 4x - 5y = -1 \)[/tex].
- The [tex]\( x \)[/tex]-intercept is [tex]\(\left( \frac{-1}{4}, 0 \right) \)[/tex].
- The [tex]\( y \)[/tex]-intercept is [tex]\(\left( 0, \frac{1}{5} \right) \)[/tex].
The provided equation is: [tex]\( 4x - 5y = -1 \)[/tex].
### Finding the [tex]\( x \)[/tex]-intercept
To find the [tex]\( x \)[/tex]-intercept, set [tex]\( y = 0 \)[/tex]:
[tex]\[ 4x - 5(0) = -1 \][/tex]
[tex]\[ 4x = -1 \][/tex]
[tex]\[ x = \frac{-1}{4} \][/tex]
So, the [tex]\( x \)[/tex]-intercept is [tex]\(\left( \frac{-1}{4}, 0 \right)\)[/tex].
### Finding the [tex]\( y \)[/tex]-intercept
To find the [tex]\( y \)[/tex]-intercept, set [tex]\( x = 0 \)[/tex]:
[tex]\[ 4(0) - 5y = -1 \][/tex]
[tex]\[ -5y = -1 \][/tex]
[tex]\[ y = \frac{-1}{-5} \][/tex]
[tex]\[ y = \frac{1}{5} \][/tex]
So, the [tex]\( y \)[/tex]-intercept is [tex]\(\left( 0, \frac{1}{5} \right)\)[/tex].
### Summary:
- The equation of the line is [tex]\( 4x - 5y = -1 \)[/tex].
- The [tex]\( x \)[/tex]-intercept is [tex]\(\left( \frac{-1}{4}, 0 \right) \)[/tex].
- The [tex]\( y \)[/tex]-intercept is [tex]\(\left( 0, \frac{1}{5} \right) \)[/tex].
