Question

what is the slope of the line that goes through points a and b? use the coordinates of points a and b to write an expression to represent the slope of the line. point a: (-3, 3) point b: (5, 1) slope = \frac{vertical distance}{horizontal distance} = \frac{\square - \square}{\square - \square}

Explanation:

Step1: Recall slope formula

Slope = $\frac{y_2 - y_1}{x_2 - x_1}$ for points $(x_1,y_1),(x_2,y_2)$

Step2: Assign coordinates

Let $(x_1,y_1)=(-3,3)$, $(x_2,y_2)=(5,1)$

Step3: Plug values into formula

$\text{Slope} = \frac{1 - 3}{5 - (-3)}$

Step4: Simplify the expression

$\frac{1 - 3}{5 + 3} = \frac{-2}{8} = -\frac{1}{4}$

Answer:

Slope expression: $\boldsymbol{\frac{1 - 3}{5 - (-3)}}$
Final slope: $\boldsymbol{-\frac{1}{4}}$