Question

slope of a line on a graph
what is the slope of the line on the graph?
○ 1
○ 1/2
○ 2
○ 3

Explanation:

Step1: Identify two points on the line

From the graph, we can see that the line passes through \((0, 3)\) and \((2, 4)\)? Wait, no, let's check again. Wait, maybe better points: Let's find two clear points. The line crosses the y - axis at \((0, 3)\)? Wait, no, looking at the grid, let's take two points. Let's see, when \(x = 0\), \(y=3\)? Wait, no, maybe \((-2, 2)\) and \((0, 3)\)? Wait, no, let's use the slope formula \(m=\frac{y_2 - y_1}{x_2 - x_1}\). Let's take two points: Let's say \((0, 3)\) and \((2, 4)\)? No, wait, maybe \((-2, 2)\) and \((0, 3)\). Wait, the difference in \(y\) is \(3 - 2=1\), difference in \(x\) is \(0 - (-2)=2\)? No, that's not right. Wait, maybe I made a mistake. Wait, let's look at the line. Let's take two points: when \(x = - 2\), \(y = 2\); when \(x = 0\), \(y = 3\)? No, wait, the line passes through \((0, 3)\) and \((2, 4)\)? Wait, no, let's check the slope formula correctly. Wait, another approach: the slope \(m=\frac{\text{rise}}{\text{run}}\). Let's find two points where the line crosses the grid intersections. Let's take \((-2, 2)\) and \((0, 3)\). The rise is \(3 - 2 = 1\), run is \(0 - (-2)=2\)? No, that would be \(1/2\)? Wait, no, maybe I got the points wrong. Wait, let's look again. Wait, the line passes through \((0, 3)\) and \((2, 4)\)? No, wait, the y - intercept is at \(y = 3\) when \(x = 0\), and when \(x = 2\), what's \(y\)? Wait, maybe the points are \((0, 3)\) and \((2, 4)\)? No, the slope would be \(\frac{4 - 3}{2 - 0}=\frac{1}{2}\)? But that's not matching. Wait, maybe I made a mistake. Wait, let's take two points: \((-2, 2)\) and \((0, 3)\). The change in \(y\) is \(3 - 2 = 1\), change in \(x\) is \(0 - (-2)=2\), so slope is \(1/2\)? But the options include \(1/2\). Wait, let's confirm. The slope formula is \(m=\frac{y_2 - y_1}{x_2 - x_1}\). Let's take two points: Let's say \((x_1,y_1)=(-2,2)\) and \((x_2,y_2)=(0,3)\). Then \(m=\frac{3 - 2}{0 - (-2)}=\frac{1}{2}\). So the slope is \(1/2\).

Step2: Confirm the slope

Using the two points \((-2, 2)\) and \((0, 3)\), the difference in \(y\) (rise) is \(3 - 2 = 1\), the difference in \(x\) (run) is \(0 - (-2)=2\). So slope \(m=\frac{\text{rise}}{\text{run}}=\frac{1}{2}\).

Answer:

\(\frac{1}{2}\) (corresponding to the option with \(1/2\))