Question

directions: find the slope from the given graph.
9)
(graph of a line on a coordinate grid)

Explanation:

Step1: Identify two points

From the graph, let's take two clear points on the line. Let's say the line passes through \((0, -1)\) and \((3, 0)\) (we can check the grid intersections).

Step2: Use slope formula

The slope formula is \(m = \frac{y_2 - y_1}{x_2 - x_1}\). Substituting \(x_1 = 0\), \(y_1 = -1\), \(x_2 = 3\), \(y_2 = 0\) into the formula: \(m=\frac{0 - (-1)}{3 - 0}=\frac{1}{3}\). Wait, maybe I misread the points. Let's re - examine. Alternatively, if we take two points: when \(x=-3\), \(y = - 2\)? No, maybe better to use the rise over run. Let's see the line: from the y - intercept (let's say it's at \((0,-1)\)) and another point. Wait, maybe the correct points are \((0, - 1)\) and \((3,0)\) is wrong. Wait, looking at the graph, the line crosses the y - axis at \((0, - 1)\) and let's find another point. If we move 3 units to the right (run = 3) and 1 unit up (rise = 1), then slope \(m=\frac{rise}{run}=\frac{1}{3}\)? Wait, no, maybe I made a mistake. Wait, let's check again. Wait, the line: let's take two points. Let's say when \(x = - 3\), \(y=-2\) and when \(x = 3\), \(y = 0\). Then \(m=\frac{0-(-2)}{3 - (-3)}=\frac{2}{6}=\frac{1}{3}\). Yes, that makes sense. So the slope is \(\frac{1}{3}\). Wait, maybe the initial points were misidentified. Let's do it properly. The slope formula is \(m=\frac{\Delta y}{\Delta x}\), where \(\Delta y\) is the change in y and \(\Delta x\) is the change in x. Let's pick two points on the line. Let's say the line passes through \((-3, - 2)\) and \((3,0)\). Then \(\Delta y=0 - (-2)=2\), \(\Delta x = 3-(-3)=6\), so \(m=\frac{2}{6}=\frac{1}{3}\).

Answer:

\(\frac{1}{3}\)