Question

find the slope of the given line, if it is defined.
the line through (0, -5) and (-8, -17)

select the correct choice below and, if necessary, fill in the answer box to complete your choice.
a. the slope is
(type an integer or a simplified fraction.)
b. the slope of the line is undefined.

Explanation:

Step1: Recall the slope formula

The slope \( m \) of a line passing through two points \( (x_1, y_1) \) and \( (x_2, y_2) \) is given by \( m=\frac{y_2 - y_1}{x_2 - x_1} \).
Here, \( (x_1, y_1)=(0, - 5) \) and \( (x_2, y_2)=(-8, - 17) \).

Step2: Substitute the values into the formula

Substitute \( x_1 = 0,y_1=-5,x_2=-8,y_2 = - 17 \) into the slope formula:
\( m=\frac{-17-(-5)}{-8 - 0}=\frac{-17 + 5}{-8}=\frac{-12}{-8} \)

Step3: Simplify the fraction

Simplify \( \frac{-12}{-8} \) by dividing both the numerator and the denominator by their greatest common divisor, which is 4.
\( \frac{-12\div4}{-8\div4}=\frac{-3}{-2}=\frac{3}{2} \)

Answer:

\( \frac{3}{2} \)