Question

what is the slope of the line that passes through the points (3, 2) and (19, 6)? 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 coordinates

Here, \( x_1 = 3 \), \( y_1 = 2 \), \( x_2 = 19 \), and \( y_2 = 6 \).

Step3: Substitute into the formula

Substitute the values into the slope formula: \( m=\frac{6 - 2}{19 - 3} \).

Step4: Simplify the numerator and denominator

Simplify the numerator: \( 6 - 2 = 4 \). Simplify the denominator: \( 19 - 3 = 16 \). So, \( m=\frac{4}{16} \).

Step5: Reduce the fraction

Reduce \(\frac{4}{16}\) by dividing both the numerator and denominator by their greatest common divisor, which is 4. \(\frac{4\div4}{16\div4}=\frac{1}{4}\).

Answer:

\(\frac{1}{4}\)