Question

what is the slope of the line?

Explanation:

Step1: Identify two points on the line

From the graph, we can see that the line passes through \((0, -2)\) and \((-2, 0)\). Let's denote \((x_1, y_1) = (0, -2)\) and \((x_2, y_2) = (-2, 0)\).

Step2: Use the slope formula

The slope \(m\) of a line passing through two points \((x_1, y_1)\) and \((x_2, y_2)\) is given by the formula \(m=\frac{y_2 - y_1}{x_2 - x_1}\).

Substitute the values of \(x_1, y_1, x_2, y_2\) into the formula:
\(m=\frac{0 - (-2)}{-2 - 0}=\frac{0 + 2}{-2}=\frac{2}{-2}=- 1\)? Wait, no, wait. Wait, maybe I mixed up the points. Wait, let's check the graph again. Wait, the x - axis and y - axis: Wait, the standard coordinate system is \(x\) horizontal and \(y\) vertical. Wait, in the given graph, the \(x\) - axis is vertical (down - up) and \(y\) - axis is horizontal (left - right)? Wait, that's a bit confusing. Wait, let's re - identify the points. Let's take two clear points. Let's see, when \(x = 0\) (the vertical line, which is the \(x\) - axis here? Wait, no, maybe the axes are labeled differently. Wait, the blue line: let's find two points. Let's see, when \(y = 0\) (the horizontal line, \(y\) - axis), the line crosses \(y = 0\) at \(x=-2\)? Wait, no, maybe I got the axes reversed. Wait, in the standard graph, \(x\) is horizontal (left - right) and \(y\) is vertical (up - down). But in the given image, the \(x\) - axis is drawn vertically (with arrows up and down) and \(y\) - axis horizontally (arrows left and right). So let's re - assign: Let's let the horizontal axis be \(y\) and vertical axis be \(x\). So a point \((x,y)\) where \(x\) is vertical (up - down) and \(y\) is horizontal (left - right). So let's take two points: when \(x = 0\) (on the vertical \(x\) - axis), \(y=-2\) (so the point is \((0, - 2)\) where \(x = 0\), \(y=-2\)). Another point: when \(y = 0\) (on the horizontal \(y\) - axis), \(x=-2\)? No, wait, the blue line passes through \((x = 0,y=-2)\) and \((x=-2,y = 0)\)? Wait, no, let's calculate the slope correctly. Wait, maybe the axes are standard, but the labels are swapped. Wait, maybe the vertical axis is \(y\) and horizontal is \(x\), but the labels are written in a rotated way. Let's assume the standard coordinate system: horizontal is \(x\), vertical is \(y\). Then, looking at the graph, the line passes through \((0, - 2)\) (when \(x = 0\), \(y=-2\)) and \((2,0)\) (when \(x = 2\), \(y = 0\))? Wait, no, let's count the grid. Let's take two points: Let's say \((x_1,y_1)=(0, - 2)\) and \((x_2,y_2)=(2,0)\). Then the slope \(m=\frac{y_2 - y_1}{x_2 - x_1}=\frac{0-(-2)}{2 - 0}=\frac{2}{2}=1\). Ah, that makes sense. I think I misread the axes. Let's confirm: from \((0, - 2)\) to \((2,0)\), the rise is \(0 - (-2)=2\) and the run is \(2 - 0 = 2\), so slope \(m=\frac{rise}{run}=\frac{2}{2}=1\).

Wait, let's take another pair of points. Let's take \((-2, - 4)\) and \((0, - 2)\). Then \(y_2-y_1=-2-(-4)=2\), \(x_2 - x_1=0-(-2)=2\), so \(m = \frac{2}{2}=1\). Yes, that's correct. So the slope is 1.

Answer:

1