Question

what is the slope of the line that goes through points a and b? whats another way to write the slope of line m? point a: (-3, 3) point b: (5, 1) slope = \frac{vertical distance}{horizontal distance} = \frac{1 - 3}{5 - (-3)} = \frac{-2}{8} = \square \frac{1}{2} \\ -\frac{1}{2} \\ \frac{1}{4} \\ -\frac{1}{4}

Explanation:

Step1: Simplify the slope fraction

$\frac{-2}{8} = \frac{-2\div2}{8\div2}$

Step2: State the simplified result

$\frac{-2\div2}{8\div2} = -\frac{1}{4}$

Step3: Identify equivalent slope form

Reverse the order of subtraction: $\frac{3-1}{-3-5} = \frac{2}{-8} = -\frac{1}{4}$

Answer:

The slope of the line through A and B is $-\frac{1}{4}$. Another way to write the slope is $\frac{3-1}{-3-5}$ (or any equivalent fraction simplifying to $-\frac{1}{4}$).