Question

what is the slope of the line that passes through the points (6, 7) and (16, 22)? write your answer in simplest form.

Explanation:

Step1: Recall 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 coordinates

Let \( (x_1, y_1)=(6, 7) \) and \( (x_2, y_2)=(16, 22) \).

Step3: Substitute into formula

Substitute the values into the slope formula: \( m=\frac{22 - 7}{16 - 6} \).

Step4: Simplify numerator and denominator

Calculate the numerator: \( 22 - 7 = 15 \).
Calculate the denominator: \( 16 - 6 = 10 \).
So, \( m=\frac{15}{10} \).

Step5: Simplify the fraction

Simplify \( \frac{15}{10} \) by dividing numerator and denominator by their greatest common divisor, which is 5. \( \frac{15\div5}{10\div5}=\frac{3}{2} \).

Answer:

\( \frac{3}{2} \)