Question

what is the slope of the line that passes through the points (4, 8) and (8, 6)? write your answer in simplest form.

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 \( m=\frac{y_2 - y_1}{x_2 - x_1} \).

Step2: Identify the coordinates

Here, \( x_1 = 4 \), \( y_1 = 8 \), \( x_2 = 8 \), and \( y_2 = 6 \).

Step3: Substitute into the formula

Substitute these values into the slope formula: \( m=\frac{6 - 8}{8 - 4} \).

Step4: Simplify the numerator and denominator

Simplify the numerator: \( 6 - 8=-2 \).
Simplify the denominator: \( 8 - 4 = 4 \).
So, \( m=\frac{-2}{4} \).

Step5: Reduce the fraction

Reduce the fraction \( \frac{-2}{4} \) to its simplest form by dividing both the numerator and the denominator by their greatest common divisor, which is 2.
\( \frac{-2\div2}{4\div2}=\frac{-1}{2} \).

Answer:

\( -\frac{1}{2} \)