To find the slope of the line segment connecting points [tex]\( G(-2, 6) \)[/tex] and [tex]\( H(5, -3) \)[/tex], we will follow these steps:
1. Identify the coordinates of the two points:
- Point [tex]\( G \)[/tex] has coordinates [tex]\( (-2, 6) \)[/tex].
- Point [tex]\( H \)[/tex] has coordinates [tex]\( (5, -3) \)[/tex].
2. Calculate the difference in the y-coordinates (Δy):
- [tex]\( \Delta y = y_2 - y_1 \)[/tex]
- Here, [tex]\( y_1 = 6 \)[/tex] (from point [tex]\( G \)[/tex]) and [tex]\( y_2 = -3 \)[/tex] (from point [tex]\( H \)[/tex]).
- [tex]\( \Delta y = -3 - 6 \)[/tex]
- [tex]\( \Delta y = -9 \)[/tex]
3. Calculate the difference in the x-coordinates (Δx):
- [tex]\( \Delta x = x_2 - x_1 \)[/tex]
- Here, [tex]\( x_1 = -2 \)[/tex] (from point [tex]\( G \)[/tex]) and [tex]\( x_2 = 5 \)[/tex] (from point [tex]\( H \)[/tex]).
- [tex]\( \Delta x = 5 - (-2) \)[/tex]
- [tex]\( \Delta x = 5 + 2 \)[/tex]
- [tex]\( \Delta x = 7 \)[/tex]
4. Calculate the slope (m):
- The slope formula is given by [tex]\( m = \frac{\Delta y}{\Delta x} \)[/tex]
- Substitute the values for [tex]\( \Delta y \)[/tex] and [tex]\( \Delta x \)[/tex]:
- [tex]\( m = \frac{-9}{7} \)[/tex]
- The slope [tex]\( m \)[/tex] can be approximated as [tex]\( -1.2857142857142858 \)[/tex]
Thus, the detailed step-by-step computation for the slope of line segment GH using points [tex]\( G(-2, 6) \)[/tex] and [tex]\( H(5, -3) \)[/tex] yields the slope approximately equal to [tex]\( -1.2857142857142858 \)[/tex].
