Certainly! To determine the slope of the given linear relationship, let's walk through the process step-by-step.
1. Understand that in the equation of a line, typically written as [tex]\( y = mx + b \)[/tex], the slope is represented by [tex]\( m \)[/tex]. The slope describes how steep the line is and in which direction it tilts.
2. For the given linear relationship with the slope specified as [tex]\( -\frac{3}{4} \)[/tex], we need to evaluate this fraction.
3. The slope [tex]\( -\frac{3}{4} \)[/tex] means that for every 4 units you move horizontally to the right on the x-axis, the y-value decreases by 3 units.
4. The fraction [tex]\( -\frac{3}{4} \)[/tex] can be converted to a decimal to make it easier to visualize and understand.
5. When we convert [tex]\( -\frac{3}{4} \)[/tex] to decimal form, it becomes [tex]\( -0.75 \)[/tex].
So, the slope of the linear relationship is [tex]\(-0.75\)[/tex]. This value indicates that the line decreases by 0.75 units for each unit increase in the horizontal direction.
