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Sagot :
To determine the slope of the line containing the points [tex]\( J(1, -4) \)[/tex] and [tex]\( K(-2, 8) \)[/tex], we will use the slope formula:
[tex]\[ m = \frac{y_2 - y_1}{x_2 - x_1} \][/tex]
where [tex]\((x_1, y_1)\)[/tex] and [tex]\((x_2, y_2)\)[/tex] are the coordinates of the two points. Here, let:
- [tex]\( J(1, -4) \)[/tex] correspond to [tex]\((x_1, y_1) = (1, -4) \)[/tex]
- [tex]\( K(-2, 8) \)[/tex] correspond to [tex]\((x_2, y_2) = (-2, 8) \)[/tex]
Plugging the values into the slope formula, we get:
[tex]\[ m = \frac{8 - (-4)}{-2 - 1} \][/tex]
Simplify inside the parentheses:
[tex]\[ m = \frac{8 + 4}{-2 - 1} \][/tex]
[tex]\[ m = \frac{12}{-3} \][/tex]
Now, divide [tex]\( 12 \)[/tex] by [tex]\(-3\)[/tex]:
[tex]\[ m = -4 \][/tex]
Thus, the slope of the line containing points [tex]\( J \)[/tex] and [tex]\( K \)[/tex] is
[tex]\[ \boxed{-4} \][/tex]
Therefore, the correct answer is A. -4.
[tex]\[ m = \frac{y_2 - y_1}{x_2 - x_1} \][/tex]
where [tex]\((x_1, y_1)\)[/tex] and [tex]\((x_2, y_2)\)[/tex] are the coordinates of the two points. Here, let:
- [tex]\( J(1, -4) \)[/tex] correspond to [tex]\((x_1, y_1) = (1, -4) \)[/tex]
- [tex]\( K(-2, 8) \)[/tex] correspond to [tex]\((x_2, y_2) = (-2, 8) \)[/tex]
Plugging the values into the slope formula, we get:
[tex]\[ m = \frac{8 - (-4)}{-2 - 1} \][/tex]
Simplify inside the parentheses:
[tex]\[ m = \frac{8 + 4}{-2 - 1} \][/tex]
[tex]\[ m = \frac{12}{-3} \][/tex]
Now, divide [tex]\( 12 \)[/tex] by [tex]\(-3\)[/tex]:
[tex]\[ m = -4 \][/tex]
Thus, the slope of the line containing points [tex]\( J \)[/tex] and [tex]\( K \)[/tex] is
[tex]\[ \boxed{-4} \][/tex]
Therefore, the correct answer is A. -4.
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