Certainly! Let's find the slope of the given line [tex]\(5x - 4y = 24\)[/tex].
1. Rearrange the equation of the line:
We start with the standard form of the line equation:
[tex]\[
5x - 4y = 24
\][/tex]
2. Solve for [tex]\(y\)[/tex] to get the equation in slope-intercept form [tex]\(y = mx + b\)[/tex], where [tex]\(m\)[/tex] is the slope:
[tex]\[
5x - 4y = 24
\][/tex]
Subtract [tex]\(5x\)[/tex] from both sides:
[tex]\[
-4y = -5x + 24
\][/tex]
Divide every term by [tex]\(-4\)[/tex]:
[tex]\[
y = \frac{5}{4}x - 6
\][/tex]
3. Identify the slope from the slope-intercept form [tex]\(y = mx + b\)[/tex]:
The coefficient of [tex]\(x\)[/tex] is the slope [tex]\(m\)[/tex].
[tex]\[
y = \left( \frac{5}{4} \right) x - 6
\][/tex]
Therefore, the slope [tex]\(m\)[/tex] is [tex]\(\frac{5}{4}\)[/tex].
Now we can select the correct option that corresponds to the slope:
[tex]\[
\boxed{\frac{5}{4}}
\][/tex]
So the correct answer is [tex]\( \boxed{E} \)[/tex].
