Question

use the two points to find the slope of this line. m = - ?/ remember: slope = rise/run

Explanation:

Step1: Identify the two points

From the graph, the two points are \((1, 2)\) and \((3, 1)\).

Step2: Calculate the rise and run

Rise is the change in \(y\)-values: \(1 - 2=- 1\). Run is the change in \(x\)-values: \(3 - 1 = 2\). But since slope \(m=\frac{\text{rise}}{\text{run}}\), here the slope can also be calculated by looking at the change from the first point to the second. The vertical change (rise) is \(1 - 2=-1\) (or we can think of it as going down 1, so rise is \(- 1\)) and horizontal change (run) is \(3 - 1 = 2\). But the formula is \(m=\frac{y_2 - y_1}{x_2 - x_1}\). Let \((x_1,y_1)=(1,2)\) and \((x_2,y_2)=(3,1)\), then \(m=\frac{1 - 2}{3 - 1}=\frac{-1}{2}\), so the slope is \(-\frac{1}{2}\), which means the numerator (the "?") is 1 and the denominator is 2.

Answer:

The numerator (the value in the green box) is \(1\) and the denominator (the value in the brown box) is \(2\), so the slope is \(-\frac{1}{2}\), with the numerator being \(1\) and denominator \(2\). If we are to fill the boxes, the green box (numerator) is \(1\) and the brown box (denominator) is \(2\).