To determine the slope of the line given by the equation [tex]\( 5x - 4y = 24 \)[/tex], we need to convert this equation into the slope-intercept form, which is [tex]\( y = mx + b \)[/tex], where [tex]\( m \)[/tex] represents the slope and [tex]\( b \)[/tex] represents the y-intercept.
Here's a step-by-step process:
1. Start with the given equation:
[tex]\[
5x - 4y = 24
\][/tex]
2. Isolate the [tex]\( y \)[/tex]-term on one side of the equation. First, subtract [tex]\( 5x \)[/tex] from both sides:
[tex]\[
-4y = -5x + 24
\][/tex]
3. Solve for [tex]\( y \)[/tex] by dividing each term by [tex]\(-4\)[/tex]:
[tex]\[
y = \frac{-5x + 24}{-4}
\][/tex]
4. Simplify the equation by distributing the division:
[tex]\[
y = \frac{-5}{-4}x + \frac{24}{-4}
\][/tex]
5. Simplify the fractions:
[tex]\[
y = \frac{5}{4}x - 6
\][/tex]
The equation is now in slope-intercept form [tex]\( y = mx + b \)[/tex]. From this form, we can identify the slope [tex]\( m \)[/tex].
The slope [tex]\( m \)[/tex] is:
[tex]\[
\frac{5}{4}
\][/tex]
Therefore, the correct answer is:
[tex]\[
\boxed{\frac{5}{4}}
\][/tex]
