Question

find the slope of the line that passes through (10, 7) and (4, 14). simplify your answer and write it as a proper fraction, improper fraction, or integer.

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, \( (x_1, y_1)=(10, 7) \) and \( (x_2, y_2)=(4, 14) \).

Step2: Substitute the values into the formula

Substitute \( x_1 = 10 \), \( y_1 = 7 \), \( x_2 = 4 \), and \( y_2 = 14 \) into the slope formula:
\( m=\frac{14 - 7}{4 - 10} \)

Step3: Simplify the numerator and the denominator

First, simplify the numerator: \( 14 - 7=7 \)
Then, simplify the denominator: \( 4 - 10=- 6 \)
So, \( m = \frac{7}{-6}=-\frac{7}{6} \)

Answer:

\(-\frac{7}{6}\)