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Sagot :
To find the slope, or rate of change, of the line containing the points [tex]\((6, -1)\)[/tex] and [tex]\((0, -7)\)[/tex], we use the slope formula:
[tex]\[ \text{slope} = \frac{y_2 - y_1}{x_2 - x_1} \][/tex]
Here, the coordinates of the two points are:
[tex]\[ (x_1, y_1) = (6, -1) \quad \text{and} \quad (x_2, y_2) = (0, -7) \][/tex]
First, substitute the coordinates into the slope formula:
[tex]\[ \text{slope} = \frac{-7 - (-1)}{0 - 6} \][/tex]
Simplify within the numerator and denominator:
Numerator:
[tex]\[ -7 - (-1) = -7 + 1 = -6 \][/tex]
Denominator:
[tex]\[ 0 - 6 = -6 \][/tex]
Thus, the slope calculation becomes:
[tex]\[ \text{slope} = \frac{-6}{-6} \][/tex]
Simplify the fraction:
[tex]\[ \frac{-6}{-6} = 1 \][/tex]
Hence, the slope (rate of change) of the line containing the points [tex]\((6, -1)\)[/tex] and [tex]\((0, -7)\)[/tex] is:
[tex]\[ \boxed{1} \][/tex]
[tex]\[ \text{slope} = \frac{y_2 - y_1}{x_2 - x_1} \][/tex]
Here, the coordinates of the two points are:
[tex]\[ (x_1, y_1) = (6, -1) \quad \text{and} \quad (x_2, y_2) = (0, -7) \][/tex]
First, substitute the coordinates into the slope formula:
[tex]\[ \text{slope} = \frac{-7 - (-1)}{0 - 6} \][/tex]
Simplify within the numerator and denominator:
Numerator:
[tex]\[ -7 - (-1) = -7 + 1 = -6 \][/tex]
Denominator:
[tex]\[ 0 - 6 = -6 \][/tex]
Thus, the slope calculation becomes:
[tex]\[ \text{slope} = \frac{-6}{-6} \][/tex]
Simplify the fraction:
[tex]\[ \frac{-6}{-6} = 1 \][/tex]
Hence, the slope (rate of change) of the line containing the points [tex]\((6, -1)\)[/tex] and [tex]\((0, -7)\)[/tex] is:
[tex]\[ \boxed{1} \][/tex]
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