Question

what is the slope of the line that passes through the points (7, -5) and (16, 7)? write your answer in simplest form.

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 \( (x_1, y_1)=(7, - 5) \) and \( (x_2, y_2)=(16, 7) \).

Step3: Substitute into formula

Substitute the values into the slope formula: \( m=\frac{7 - (-5)}{16 - 7}=\frac{7 + 5}{9}=\frac{12}{9} \).

Step4: Simplify the fraction

Simplify \( \frac{12}{9} \) by dividing numerator and denominator by their greatest common divisor, which is 3. So \( \frac{12\div3}{9\div3}=\frac{4}{3} \).

Answer:

\( \frac{4}{3} \)