To find the slope of line GH that passes through points G(-2, 6) and H(5, -3), you use the slope formula. The slope formula is given as:
[tex]\[ \text{slope} = \frac{{y_2 - y_1}}{{x_2 - x_1}} \][/tex]
Here, [tex]\((x_1, y_1)\)[/tex] are the coordinates of point G, and [tex]\((x_2, y_2)\)[/tex] are the coordinates of point H.
1. Identify the coordinates of the points:
- For point G: [tex]\((x_1, y_1) = (-2, 6)\)[/tex]
- For point H: [tex]\((x_2, y_2) = (5, -3)\)[/tex]
2. Substitute these coordinates into the slope formula:
[tex]\[ \text{slope} = \frac{{-3 - 6}}{{5 - (-2)}} \][/tex]
3. Simplify the expression:
[tex]\[ \text{slope} = \frac{{-3 - 6}}{{5 + 2}} \][/tex]
[tex]\[ \text{slope} = \frac{{-9}}{{7}} \][/tex]
4. Perform the division to find the slope in decimal form:
[tex]\[ \text{slope} \approx -1.2857142857142858 \][/tex]
Thus, the slope of the line GH is approximately [tex]\(-1.2857142857142858\)[/tex].
