Question

interpreting slope - item 21024
what is the slope of the line shown?
image of a coordinate grid with a red line
clear check
slope = $-\frac{1}{2}$
slope = 7
slope = 2
slope = -2

Explanation:

Step1: Identify two points on the line

From the graph, we can see two clear points: let's take \((-1, 8)\) and \((0, 6)\) (or other visible points, but these are easy to identify). Wait, actually, looking at the intercepts: when \(x = 0\), \(y = 8\)? Wait, no, maybe better to take two points with integer coordinates. Let's see, the line passes through \((-1, 8)\) and \((0, 6)\)? Wait, no, maybe \((0, 8)\) and \((1, 6)\)? Wait, no, let's check the grid. Each square is 1 unit. Let's take two points: say \((-1, 8)\) and \((1, 4)\)? Wait, maybe a better approach: use the slope formula \(m=\frac{y_2 - y_1}{x_2 - x_1}\). Let's pick two points: when \(x = -1\), \(y = 8\) (top left red dot) and when \(x = 4\), \(y = -2\) (the x-intercept? Wait, no, the x-intercept is at \(x = 4\), \(y = 0\)? Wait, maybe I made a mistake. Wait, the line goes from \((-1, 8)\) to \((4, -2)\)? No, let's count the rise over run. From \((-1, 8)\) to \((0, 6)\): the change in \(y\) is \(6 - 8=-2\), change in \(x\) is \(0 - (-1)=1\), so slope is \(\frac{-2}{1}=-2\). Wait, that's one way. Alternatively, from \((0, 8)\) to \((1, 6)\): change in \(y\) is \(6 - 8=-2\), change in \(x\) is \(1 - 0 = 1\), so slope is \(-2\). So the slope is \(-2\).

Step2: Match with the options

The options are \(slope = -\frac{1}{2}\), \(slope = 7\), \(slope = 2\), \(slope = -2\). So the correct one is \(slope = -2\).

Answer:

The correct option is the one with \(slope = -2\) (the bottom right option, with the radio button next to it). So the answer is the option labeled "slope = -2" (the fourth option, assuming the options are: top left: \(slope = -\frac{1}{2}\), top right: \(slope = 7\), bottom left: \(slope = 2\), bottom right: \(slope = -2\)). So the answer is the option with \(slope = -2\), i.e., the one with the radio button at the bottom right, labeled "slope = -2".