Question

find the slope of the line graphed below.

Explanation:

Step1: Identify two points on the line

From the graph, we can see two points: $(-4, 5)$ and $(2, 1)$ (assuming the coordinates are read correctly from the grid).

Step2: Use the slope formula

The slope formula is $m = \frac{y_2 - y_1}{x_2 - x_1}$. Let $(x_1, y_1) = (-4, 5)$ and $(x_2, y_2) = (2, 1)$. Then:
$$m = \frac{1 - 5}{2 - (-4)} = \frac{-4}{6} = -\frac{2}{3}$$

Wait, maybe I misread the points. Let's re - check. Looking at the graph again, the two marked points: one seems to be $(-4,5)$ and the other $(2,1)$? Wait, no, maybe the y - axis and x - axis are labeled differently. Wait, the x - axis is the horizontal axis (usually right - positive) and y - axis vertical (up - positive). Wait, maybe the points are $(-4,5)$ and $(2,1)$? Wait, no, let's count the grid. From $(-4,5)$ to $(2,1)$: the change in y is $1 - 5=-4$, change in x is $2-(-4) = 6$. So slope is $\frac{-4}{6}=-\frac{2}{3}$? Wait, no, maybe I got the points wrong. Wait, another way: let's take the two points as $(-4,5)$ and $(2,1)$. Wait, or maybe $( - 4,5)$ and $(2,1)$: the run (x - change) is $2-(-4)=6$, rise (y - change) is $1 - 5=-4$. So slope is $\frac{-4}{6}=-\frac{2}{3}$. Wait, but maybe the points are $(-4,5)$ and $(2,1)$? Wait, no, maybe I made a mistake in the coordinates. Let's look at the graph again. The first point: x = - 4, y = 5 (since it's on the horizontal line y = 5, x=-4). The second point: x = 2, y = 1 (on the horizontal line y = 1, x = 2). So the difference in y: $1 - 5=-4$, difference in x: $2-(-4)=6$. So slope is $\frac{-4}{6}=-\frac{2}{3}$. Wait, but maybe the points are different. Wait, maybe the y - axis is labeled with positive up, x - axis positive right. So from $(-4,5)$ to $(2,1)$: the slope is $\frac{1 - 5}{2-(-4)}=\frac{-4}{6}=-\frac{2}{3}$.

Wait, maybe I misread the points. Let's check again. The two blue dots: one is at x=-4, y = 5 (since it's 4 units left of the origin on x - axis, 5 units up on y - axis). The other is at x = 2, y = 1 (2 units right of origin, 1 unit up). So the change in y (Δy) is $1 - 5=-4$, change in x (Δx) is $2-(-4)=6$. So slope $m=\frac{\Delta y}{\Delta x}=\frac{-4}{6}=-\frac{2}{3}$.

Answer:

$-\frac{2}{3}$