Question

what is the slope of this line? simplify your answer completely. slope = - ?/? slope: rise/run

Explanation:

Step1: Identify two points

The two points on the line are \((-2, 0)\) and \((-1, -2)\).

Step2: Calculate rise and run

Rise is the change in \(y\): \(-2 - 0 = -2\).
Run is the change in \(x\): \(-1 - (-2) = 1\).

Step3: Compute slope

Slope \(= \frac{\text{rise}}{\text{run}} = \frac{-2}{1} = -2\). But the given form is \( \text{Slope} = -\frac{[?]}{[?]} \), so we can also calculate as \( \frac{0 - (-2)}{-2 - (-1)} = \frac{2}{-1} = -2\), or in the form \( -\frac{2}{1} \) (matching the given structure where the numerator is the boxed part). Wait, let's re - check the points. Wait, maybe I misread the points. Wait, the first point: when \(x = - 2\), \(y = 0\); the second point: when \(x=-1\), \(y = - 2\)? Wait, no, looking at the graph, the second point is at \(x=-1\), \(y = - 2\)? Wait, no, the grid: the first point is \((-2,0)\), the second point is \((-1, - 2)\)? Wait, no, let's count the grid squares. From \((-2,0)\) to \((-1,-2)\): the change in \(y\) is \(-2 - 0=-2\), change in \(x\) is \(-1-(-2) = 1\). So slope is \(\frac{-2}{1}=-2\), which can be written as \( -\frac{2}{1} \). So the numerator is 2 and denominator is 1.

Answer:

The slope is \( -\frac{2}{1} \), so the value in the numerator box is 2 and denominator is 1. But if we consider the form \( \text{Slope}=-\frac{[?]}{[?]} \), the answer for the numerator (the? in the numerator) is 2 and denominator is 1. But since the problem has \( \text{Slope}=-\frac{[?]}{[?]} \), and we found that the slope is \(-2=-\frac{2}{1}\), so the numerator (the? in the numerator) is 2.