Question

which describes the slope of the given line? options: positive, negative, zero, undefined

Explanation:

Step1: Identify two points on the line

From the graph, we can see two points: let's take \((-1, 0)\) and \((5, -4)\) (or other visible points). Wait, actually, looking at the axes, let's re - identify. Let's take the point where \(x=-1,y = 0\) and another point, say when \(x = 5,y=-4\)? Wait, no, maybe better to take two clear points. Let's see, the line passes through \((-1,0)\) and \((2, - 2)\)? Wait, maybe I made a mistake. Wait, the x - axis and y - axis: the y - axis is horizontal? Wait, no, in the graph, the horizontal axis is y - axis? Wait, no, usually, the horizontal axis is x - axis and vertical is y - axis, but in this graph, the labels seem reversed? Wait, the arrow for y is horizontal? Wait, maybe the graph has x - axis vertical and y - axis horizontal? Wait, the line has a negative slope. Let's use the slope formula \(m=\frac{y_2 - y_1}{x_2 - x_1}\). Let's take two points: let's say \((x_1,y_1)=(-1,0)\) and \((x_2,y_2)=(5, - 4)\)? No, wait, when x increases (moves to the right), y decreases. So the slope is negative. Let's calculate the slope between two points. Let's take \((-1,0)\) and \((2, - 2)\). Then \(m=\frac{-2 - 0}{2-(-1)}=\frac{-2}{3}\), which is negative. Alternatively, take two points: when x = - 1, y = 0; when x = 5, y=-4. Then \(m=\frac{-4 - 0}{5-(-1)}=\frac{-4}{6}=-\frac{2}{3}\), which is negative. So the slope is negative.

Step2: Determine the sign of the slope

Since as x increases (moves from left to right), the y - value decreases (the line goes down from left to right), the slope \(m=\frac{\Delta y}{\Delta x}\) will be negative because \(\Delta y\) is negative and \(\Delta x\) is positive, so their ratio is negative.

Answer:

Negative