To find the [tex]$y$[/tex]-intercept of the equation [tex]\( 5x - 6y = 21 \)[/tex]:
1. Set [tex]\( x = 0 \)[/tex] in the equation to isolate [tex]\( y \)[/tex]:
[tex]\[5(0) - 6y = 21\][/tex]
[tex]\[ -6y = 21 \][/tex]
2. Solve for [tex]\( y \)[/tex] by dividing both sides by [tex]\(-6\)[/tex]:
[tex]\[ y = \frac{21}{-6} \][/tex]
[tex]\[ y = -\frac{21}{6} \][/tex]
[tex]\[ y = -\frac{7}{2} \][/tex]
Hence, the [tex]$y$[/tex]-intercept is [tex]\( -\frac{7}{2} \)[/tex].
To find the [tex]$x$[/tex]-intercept of the equation [tex]\( 5x - 6y = 21 \)[/tex]:
1. Set [tex]\( y = 0 \)[/tex] in the equation to isolate [tex]\( x \)[/tex]:
[tex]\[ 5x - 6(0) = 21 \][/tex]
[tex]\[ 5x = 21 \][/tex]
2. Solve for [tex]\( x \)[/tex] by dividing both sides by [tex]\( 5 \)[/tex]:
[tex]\[ x = \frac{21}{5} \][/tex]
Hence, the [tex]$x$[/tex]-intercept is [tex]\( \frac{21}{5} \)[/tex].
So, the answers are:
[tex]\[
\begin{array}{l}
y \text{-intercept: } -\frac{7}{2} \\
x \text{-intercept: } \frac{21}{5}
\end{array}
\][/tex]
