Question

find the slope of the line.

Explanation:

Step1: Identify two points on the line

From the graph, let's take two clear points. For example, $(-6, 2)$ and $(-1, -3)$ (or other visible points; let's confirm with grid). Wait, maybe better to use the formula for slope $m = \frac{y_2 - y_1}{x_2 - x_1}$. Let's pick two points: say, when $x = -5$, $y = 1$ and when $x = 0$, $y = -4$? Wait, no, looking at the line, let's take two points with integer coordinates. Let's see, the line passes through $(-6, 2)$ and $(-1, -3)$? Wait, maybe another pair. Wait, let's check the grid. Let's take the point $(-5, 1)$ and $(0, -4)$? Wait, no, maybe the slope is calculated as rise over run. Let's see, from a point to another, the change in y over change in x. Let's take two points: let's say $(-6, 2)$ and $(-1, -3)$. Then $y_2 - y_1 = -3 - 2 = -5$, $x_2 - x_1 = -1 - (-6) = 5$. So slope $m = \frac{-5}{5} = -1$? Wait, no, maybe I made a mistake. Wait, let's take another pair. Let's take $(-4, 0)$ and $(-1, -3)$. Then $y_2 - y_1 = -3 - 0 = -3$, $x_2 - x_1 = -1 - (-4) = 3$. So slope $m = \frac{-3}{3} = -1$. Wait, but the options have -1 as an option. Wait, maybe the correct slope is -1? Wait, no, wait the graph: let's see, the line is going down from left to right, so negative slope. Let's count the rise over run. From a point, say, when x increases by 1, y decreases by 1? Wait, no, let's take two points: ( -5, 1 ) and ( -4, 0 ). Then change in y is 0 - 1 = -1, change in x is -4 - (-5) = 1. So slope is -1/1 = -1. Yes, so the slope is -1.

Step2: Confirm with slope formula

Using the slope formula $m = \frac{y_2 - y_1}{x_2 - x_1}$, let's take two points on the line. Let's choose $(x_1, y_1) = (-5, 1)$ and $(x_2, y_2) = (-4, 0)$. Then $m = \frac{0 - 1}{-4 - (-5)} = \frac{-1}{1} = -1$. So the slope is -1.

Answer:

-1 (corresponding to the option with -1)