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What is the slope of the line that contains the points [tex]$(-2,7)$[/tex] and [tex]$(2,3)$[/tex]?

A. 1
B. -1
C. 4
D. -4


Sagot :

To find the slope of the line that contains the points [tex]\((-2, 7)\)[/tex] and [tex]\( (2, 3) \)[/tex], we can use the slope formula, which is given by:

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

Here, [tex]\((x_1, y_1)\)[/tex] are the coordinates of the first point, and [tex]\((x_2, y_2)\)[/tex] are the coordinates of the second point. Substituting the coordinates given in the question:

- For the first point [tex]\((-2, 7)\)[/tex], we have [tex]\(x_1 = -2\)[/tex] and [tex]\(y_1 = 7\)[/tex].
- For the second point [tex]\((2, 3)\)[/tex], we have [tex]\(x_2 = 2\)[/tex] and [tex]\(y_2 = 3\)[/tex].

Now, substitute these values into the slope formula:

[tex]\[ \text{slope} = \frac{3 - 7}{2 - (-2)} \][/tex]

Next, simplify the numerator and the denominator:

[tex]\[ \text{slope} = \frac{3 - 7}{2 + 2} = \frac{-4}{4} \][/tex]

Finally, compute the division:

[tex]\[ \text{slope} = -1 \][/tex]

Therefore, the slope of the line that contains the points [tex]\((-2, 7)\)[/tex] and [tex]\( (2, 3) \)[/tex] is [tex]\(-1\)[/tex].

Hence, the correct answer is:

B. -1