To determine the slope of the equation [tex]\( y = \frac{5}{4} x - \frac{7}{4} \)[/tex], we need to recognize that it is given in the slope-intercept form, which is:
[tex]\[ y = mx + b \][/tex]
In this form:
- [tex]\( m \)[/tex] represents the slope of the line.
- [tex]\( b \)[/tex] represents the y-intercept of the line.
For the equation [tex]\( y = \frac{5}{4} x - \frac{7}{4} \)[/tex]:
- [tex]\( m \)[/tex] is the coefficient of [tex]\( x \)[/tex].
- [tex]\( b \)[/tex] is the constant term.
Here, comparing the given equation [tex]\( y = \frac{5}{4} x - \frac{7}{4} \)[/tex] with the slope-intercept form [tex]\( y = mx + b \)[/tex]:
- The coefficient of [tex]\( x \)[/tex] is [tex]\( \frac{5}{4} \)[/tex].
- Therefore, the slope [tex]\( m \)[/tex] is [tex]\( \frac{5}{4} \)[/tex].
So, the slope of the equation is [tex]\( \frac{5}{4} \)[/tex].
[tex]\(\boxed{ \frac{5}{4} }\)[/tex]
