Question

what is the slope of the line graphed here?
options:
\\( \frac{1}{3} \\)
\\( 3 \\)
\\( -1 \\)
\\( 1 \\)

Explanation:

Step1: Identify two points on the line

From the graph, we can see that the line passes through \((-3, 0)\) and \((0, 3)\).

Step2: Use the slope formula

The slope \(m\) between two points \((x_1, y_1)\) and \((x_2, y_2)\) is given by \(m=\frac{y_2 - y_1}{x_2 - x_1}\).
Substituting \(x_1=-3\), \(y_1 = 0\), \(x_2=0\), and \(y_2 = 3\) into the formula:
\(m=\frac{3 - 0}{0-(-3)}=\frac{3}{3}=1\)? Wait, no, wait. Wait, let's check again. Wait, another pair of points: when \(x = 0\), \(y=3\); when \(x = 1\), \(y = 4\)? Wait, no, wait the graph: let's take \((-3,0)\) and \((0,3)\). Then \(y_2 - y_1=3 - 0 = 3\), \(x_2 - x_1=0-(-3)=3\), so \(m = \frac{3}{3}=1\)? Wait, but wait, maybe I made a mistake. Wait, no, let's check the y-intercept is 3, and when x increases by 1, y increases by 1? Wait, no, when x is 0, y is 3; when x is 1, y is 4? Wait, no, the grid: each square is 1 unit. So from (0,3) to (1,4): rise is 1, run is 1, so slope is 1? Wait, but the options include 1. Wait, but let's re - calculate. The slope formula is \(m=\frac{\Delta y}{\Delta x}\). Let's take two points: \((-3,0)\) and \((0,3)\). \(\Delta y=3 - 0 = 3\), \(\Delta x=0-(-3)=3\), so \(m = \frac{3}{3}=1\). Or take \((0,3)\) and \((1,4)\): \(\Delta y = 4 - 3=1\), \(\Delta x=1 - 0 = 1\), so \(m = 1\).

Answer:

1 (the option with 1, assuming the options are like the ones shown, the correct option is the one with 1)