Welcome to Westonci.ca, where you can find answers to all your questions from a community of experienced professionals. Experience the convenience of finding accurate answers to your questions from knowledgeable experts on our platform. Join our platform to connect with experts ready to provide precise answers to your questions in different areas.

Line GH contains points [tex]\( G(-2, 6) \)[/tex] and [tex]\( H(5, -3) \)[/tex]. What is the slope of [tex]\( GH \)[/tex]?

A. 6

B. 1

C. 0

D. -1


Sagot :

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].