To find the slope of the line given by the equation [tex]\( 5x - 4y = 20 \)[/tex], we will convert this equation into the slope-intercept form, [tex]\( y = mx + b \)[/tex], where [tex]\( m \)[/tex] represents the slope of the line.
Here is a step-by-step solution to find the slope:
1. Start with the given equation:
[tex]\[
5x - 4y = 20
\][/tex]
2. Rearrange the equation to solve for [tex]\( y \)[/tex]. Firstly, isolate the [tex]\( y \)[/tex]-term by moving the [tex]\( 5x \)[/tex] to the other side of the equation:
[tex]\[
-4y = -5x + 20
\][/tex]
3. Next, solve for [tex]\( y \)[/tex] by dividing every term by [tex]\(-4\)[/tex]:
[tex]\[
y = \frac{-5x + 20}{-4}
\][/tex]
4. Simplify the right-hand side:
[tex]\[
y = \frac{-5x}{-4} + \frac{20}{-4}
\][/tex]
5. This simplifies to:
[tex]\[
y = \frac{5}{4}x - 5
\][/tex]
In the slope-intercept form [tex]\( y = mx + b \)[/tex], the coefficient of [tex]\( x \)[/tex] is [tex]\( m \)[/tex], which represents the slope.
From the equation [tex]\( y = \frac{5}{4}x - 5 \)[/tex], we can see that the slope [tex]\( m \)[/tex] is [tex]\( \frac{5}{4} \)[/tex].
Thus, the slope of the line is:
[tex]\[
m = \frac{5}{4}
\][/tex]
The correct answer is:
C. [tex]\( m = \frac{5}{4} \)[/tex]
