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What is the slope of the line containing (6, -1) and (0, -7)?

Rate of change is (example: -3/5)

Answer either as an integer or a fraction; no decimals.

If the rate of change is undefined, write "undefined."


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]