Question

1 test (t2)
(1 point)
-2
1/2
2
-1/2

Explanation:

Step1: Identify two points on the line

From the graph, we can see that the line passes through the points \((0, -4)\) (the y - intercept) and \((6, -1)\). We can also use other points, for example, when \(x = 0\), \(y=-4\) and when \(x = 6\), \(y=-1\).

Step2: Use the slope formula

The slope formula is \(m=\frac{y_2 - y_1}{x_2 - x_1}\). Let \((x_1,y_1)=(0, - 4)\) and \((x_2,y_2)=(6, - 1)\).
Substitute the values into the formula: \(m=\frac{-1-(-4)}{6 - 0}=\frac{-1 + 4}{6}=\frac{3}{6}=\frac{1}{2}\)? Wait, no, maybe I made a mistake in reading the graph. Wait, let's re - examine the graph. Wait, maybe the y - intercept is at \((0,-4)\)? Wait, no, looking at the grid, each square is 1 unit. Wait, the red line: when \(x = 0\), the y - coordinate is \(-4\)? Wait, no, maybe the points are \((0,-4)\) and \((8,0)\)? No, the options have \(\frac{1}{2}\) or \(-\frac{1}{2}\)? Wait, maybe I misread the points. Wait, let's take two clear points. Let's take \((0,-4)\) and \((8,0)\)? No, the options are \(-2\), \(\frac{1}{2}\), \(2\), \(-\frac{1}{2}\). Wait, maybe the line passes through \((0,-4)\) and \((4, - 2)\). Then the slope \(m=\frac{-2-(-4)}{4-0}=\frac{2}{4}=\frac{1}{2}\)? No, the options have \(\frac{1}{2}\) as an option? Wait, the options are: \(-2\), \(\frac{1}{2}\), \(2\), \(-\frac{1}{2}\). Wait, maybe the correct points are \((0,-4)\) and \((6, - 1)\): slope is \(\frac{-1+4}{6}=\frac{3}{6}=\frac{1}{2}\). Wait, but maybe I made a mistake. Wait, another way: the slope of a line \(y = mx + b\). Let's see, if we take two points: when \(x = 0\), \(y=-4\); when \(x = 8\), \(y = 0\). Then slope \(m=\frac{0 + 4}{8-0}=\frac{4}{8}=\frac{1}{2}\). Yes, so the slope is \(\frac{1}{2}\). Wait, but the options: wait, the user's options are maybe \(-2\), \(\frac{1}{2}\), \(2\), \(-\frac{1}{2}\). So the correct answer is \(\frac{1}{2}\).

Answer:

\(\frac{1}{2}\) (assuming the options are something like A. - 2, B. \(\frac{1}{2}\), C. 2, D. \(-\frac{1}{2}\), the answer is B. \(\frac{1}{2}\))