Question

find the slope of the line that passes through (-15, 100) and (15, 8). simplify your answer and write it as a proper fraction, improper fraction, or integer.

Explanation:

Step1: Recall slope formula

The slope \( m \) between 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, \( (x_1,y_1)=(- 15,100) \) and \( (x_2,y_2)=(15,8) \).

Step2: Substitute values into formula

Substitute \( y_2 = 8 \), \( y_1=100 \), \( x_2 = 15 \), \( x_1=-15 \) into the formula:
\( m=\frac{8 - 100}{15-(-15)} \)

Step3: Simplify numerator and denominator

Simplify numerator: \( 8 - 100=-92 \)
Simplify denominator: \( 15-(-15)=15 + 15 = 30 \)
So, \( m=\frac{-92}{30} \)

Step4: Reduce the fraction

Divide numerator and denominator by their greatest common divisor, which is 2.
\( \frac{-92\div2}{30\div2}=\frac{-46}{15} \)

Answer:

\( -\frac{46}{15} \)