Question

what is the slope of this line? simplify your answer and write it as a proper fraction, improper fraction, or integer.

Explanation:

Step1: Recall slope formula

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

Step2: Identify two points on the line

From the graph, the line passes through the origin \((0, 0)\) and another point, say \((4, 3)\) (we can also use other points like \((8, 6)\), etc.). Let \((x_1, y_1)=(0, 0)\) and \((x_2, y_2)=(4, 3)\).

Step3: Calculate the slope

Substitute the values into the slope formula: \( m=\frac{3 - 0}{4 - 0}=\frac{3}{4} \)? Wait, no, wait. Wait, looking at the graph again, when \( x = 4 \), \( y = 3 \)? Wait, no, maybe I made a mistake. Wait, let's take another point. Wait, when \( x = 8 \), \( y = 6 \). So using \((0,0)\) and \((8,6)\): \( m=\frac{6 - 0}{8 - 0}=\frac{6}{8}=\frac{3}{4} \)? Wait, no, wait, the line passes through (0,0) and (4,3)? Wait, no, let's check the grid. Each grid square is 1 unit. So from (0,0) to (4,3)? Wait, no, when x=4, y=3? Wait, no, looking at the graph, the line goes through (0,0) and (4, 3)? Wait, no, maybe (2,1.5)? No, better to take integer points. Wait, (0,0) and (8,6): the rise is 6, run is 8, so slope is 6/8 = 3/4? Wait, no, wait, maybe I messed up. Wait, the line passes through (0,0) and (4, 3)? Wait, no, let's see, when x=4, y=3? Wait, the y-axis: at x=4, the y-coordinate is 3? Wait, the graph shows that at x=4, y=3? Wait, no, looking at the graph, the line goes through (0,0) and (8,6). So the slope is (6 - 0)/(8 - 0) = 6/8 = 3/4? Wait, no, wait, maybe (4,3) is correct. Wait, let's check with (0,0) and (4,3): (3-0)/(4-0)= 3/4. Alternatively, (8,6): (6-0)/(8-0)= 6/8= 3/4. Wait, but maybe I made a mistake. Wait, another way: the line passes through (0,0) and (4,3)? Wait, no, let's look at the graph again. The line is going up 3 units when x increases by 4 units? Wait, no, when x=4, y=3? Wait, the y-axis: at x=4, the y is 3? Yes, because from (0,0) to (4,3), the vertical change is 3, horizontal change is 4, so slope is 3/4. Wait, but let's confirm with another pair. ( - 4, - 3) and (0,0): slope is (0 - (-3))/(0 - (-4))= 3/4. Yes, so the slope is 3/4? Wait, no, wait, maybe I made a mistake. Wait, the line in the graph: when x=8, y=6, so 6/8= 3/4. So the slope is 3/4. Wait, but let's check again. The formula is rise over run. So from (0,0) to (8,6), rise is 6, run is 8, so 6/8= 3/4. So the slope is 3/4.

Wait, no, wait, maybe I messed up the points. Wait, the line passes through (0,0) and (4, 3)? Wait, 3/4 is correct? Wait, let's see, the line goes through (0,0) and (8,6), so slope is 6/8= 3/4. Yes.

Answer:

\(\frac{3}{4}\)