Question

find the slope of the line that passes through (1, 2) and (6, 6). simplify your answer and write it as a proper fraction, improper fraction, or integer.

Explanation:

Step1: Recall 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 coordinates

Let \( (x_1, y_1)=(1, 2) \) and \( (x_2, y_2)=(6, 6) \).

Step3: Substitute into formula

Substitute the values into the slope formula: \( m=\frac{6 - 2}{6 - 1} \).

Step4: Simplify numerator and denominator

Simplify the numerator: \( 6 - 2 = 4 \). Simplify the denominator: \( 6 - 1 = 5 \). So \( m=\frac{4}{5} \).

Answer:

\(\frac{4}{5}\)