Question

determine the slope of the line shown on the graph. type your answer in the space below. record all fractions as 3/4 or -3/4. m =

Explanation:

Step1: Identify two points on the line

Let's take two points on the line, for example, \((0, 0)\) and \((4, 1)\) (we can see from the grid that moving 4 units right and 1 unit up from the origin gives another point on the line).

Step2: Use the slope formula

The slope formula is \(m=\frac{y_2 - y_1}{x_2 - x_1}\). Substituting \(x_1 = 0\), \(y_1 = 0\), \(x_2 = 4\), \(y_2 = 1\) into the formula, we get \(m=\frac{1 - 0}{4 - 0}=\frac{1}{4}\). Wait, maybe I picked the wrong points. Let's check again. If we take two points like \((-4, -1)\) and \((4, 1)\), then \(m=\frac{1 - (-1)}{4 - (-4)}=\frac{2}{8}=\frac{1}{4}\). Or maybe the line goes through \((0,0)\) and \((8, 2)\), then \(m=\frac{2 - 0}{8 - 0}=\frac{2}{8}=\frac{1}{4}\). So the slope is \(\frac{1}{4}\)? Wait, maybe the grid is such that from the origin, moving 4 units right and 1 unit up, so rise over run is 1/4. Wait, maybe I made a mistake. Wait, the line is passing through the origin and let's see another point. Let's say when x is 4, y is 1, so slope is (1 - 0)/(4 - 0) = 1/4. Or maybe x=8, y=2, so (2-0)/(8-0)=2/8=1/4. So the slope is 1/4.

Wait, maybe the correct points are (0,0) and (4,1), so slope is 1/4. Let me confirm. The slope formula is rise over run, which is (change in y)/(change in x). So if we move from (0,0) to (4,1), change in y is 1, change in x is 4, so slope is 1/4.

Answer:

\(\frac{1}{4}\)