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 \( m \) between two points \( (x_1, y_1) \) and \( (x_2, y_2) \) is given by \( m=\frac{y_2 - y_1}{x_2 - x_1} \).

Step2: Identify the points

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

Step3: Substitute into the formula

Substitute the values into the slope formula: \( m=\frac{14 - 7}{4 - 10} \).

Step4: Simplify the numerator and denominator

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

Answer:

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