Discover new information and get your questions answered with IDNLearn.com. Find accurate and detailed answers to your questions from our experienced and dedicated community members.

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]