Question

what is the slope of the line that passes through the points (10, 8) and (7, 14)? write your answer in simplest form.

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 \( (x_1, y_1)=(10, 8) \) and \( (x_2, y_2)=(7, 14) \).

Step3: Substitute into the formula

Substitute the values into the slope formula: \( m=\frac{14 - 8}{7 - 10} \).

Step4: Simplify the numerator and denominator

Simplify the numerator: \( 14 - 8 = 6 \).
Simplify the denominator: \( 7 - 10=-3 \).
So, \( m = \frac{6}{-3} \).

Step5: Simplify the fraction

Simplify \( \frac{6}{-3}=-2 \).

Answer:

\(-2\)