Question

a line is drawn so that it passes through the points (3, 4) and (2, 1) .
what is the slope of the line?

-3
(\frac{1}{3})
3
(-\frac{1}{3})

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 \((x_1, y_1)=(3, 4)\) and \((x_2, y_2)=(2, 1)\).

Step3: Substitute into formula

Substitute the values into the slope formula: \( m=\frac{1 - 4}{2 - 3} \).

Step4: Simplify numerator and denominator

Simplify numerator: \( 1 - 4=-3 \), denominator: \( 2 - 3=-1 \). So \( m=\frac{-3}{-1}=3 \).

Answer:

3 (corresponding to the option "3")