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Find the slope of the line that passes through the points (1, 7) and (10, 1).

A. [tex]\(\frac{2}{3}\)[/tex]
B. [tex]\(-\frac{2}{3}\)[/tex]
C. [tex]\(-\frac{3}{2}\)[/tex]
D. [tex]\(\frac{3}{2}\)[/tex]

Sagot :

To find the slope of the line that passes through the points [tex]\((1, 7)\)[/tex] and [tex]\((10, 1)\)[/tex], we can use the slope formula:

[tex]\[ m = \frac{y_2 - y_1}{x_2 - x_1} \][/tex]

Here, [tex]\((x_1, y_1) = (1, 7)\)[/tex] and [tex]\((x_2, y_2) = (10, 1)\)[/tex].

1. Identify the coordinates:
[tex]\( (x_1, y_1) = (1, 7) \)[/tex]
[tex]\( (x_2, y_2) = (10, 1) \)[/tex]

2. Calculate the change in [tex]\(y\)[/tex] (rise):
[tex]\[ y_2 - y_1 = 1 - 7 = -6 \][/tex]

3. Calculate the change in [tex]\(x\)[/tex] (run):
[tex]\[ x_2 - x_1 = 10 - 1 = 9 \][/tex]

4. Plug the values from steps 2 and 3 into the slope formula:
[tex]\[ m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{-6}{9} = -\frac{2}{3} \][/tex]

So, the slope of the line that passes through the points [tex]\((1, 7)\)[/tex] and [tex]\((10, 1)\)[/tex] is:

[tex]\[ -\frac{2}{3} \][/tex]

Therefore, the correct answer is:

[tex]\[ -\frac{2}{3} \][/tex]