Question

6)
slope =
graph of a line on a coordinate plane with grid lines. the line passes through points, and theres a grid with x and y axes labeled, and the question is to find the slope.

Explanation:

Step1: Identify two points on the line

We can see that the line passes through \((-4, 3)\) and \((2, -2)\) (we can also use other points like \((0, 0)\) and \((2, -2)\) or \((-4, 3)\) and \((0, 0)\); let's use \((-4, 3)\) and \((2, -2)\) for clarity).

Step2: Use the slope formula

The slope formula is \(m=\frac{y_2 - y_1}{x_2 - x_1}\), where \((x_1,y_1)=(-4,3)\) and \((x_2,y_2)=(2,-2)\).
Substitute the values into the formula: \(m=\frac{-2 - 3}{2 - (-4)}\)

Step3: Simplify the expression

First, calculate the numerator: \(-2 - 3=-5\)
Then, calculate the denominator: \(2 - (-4)=2 + 4 = 6\)? Wait, no, wait, let's check the points again. Wait, maybe a better pair: let's take \((0,0)\) and \((2, -2)\). Then \(x_1 = 0,y_1 = 0\), \(x_2 = 2,y_2=-2\). Then \(m=\frac{-2 - 0}{2 - 0}=\frac{-2}{2}=-1\). Wait, or \((-4,3)\) and \((0,0)\): \(m=\frac{0 - 3}{0 - (-4)}=\frac{-3}{4}\)? No, that's wrong. Wait, looking at the graph, when \(x\) increases by 1, \(y\) decreases by 1? Wait, let's check the grid. From \((-4, 3)\) to \((-3, 2)\): that's a change in \(y\) of \(2 - 3=-1\), change in \(x\) of \(-3 - (-4)=1\), so slope is \(\frac{-1}{1}=-1\). Oh, I see, I made a mistake in choosing points earlier. Let's take two points with integer coordinates that are easy. Let's take \((-4, 3)\) and \((-3, 2)\). Then \(x_1=-4,y_1 = 3\), \(x_2=-3,y_2 = 2\). Then slope \(m=\frac{y_2 - y_1}{x_2 - x_1}=\frac{2 - 3}{-3 - (-4)}=\frac{-1}{1}=-1\). Alternatively, \((0,0)\) and \((1, -1)\): slope is \(\frac{-1 - 0}{1 - 0}=-1\). So the correct slope is -1.

Wait, let's do it properly. Let's pick two clear points. Let's take \((-4, 3)\) and \((4, -5)\)? No, wait the arrow is at \((4, -4)\)? Wait, the graph: the left arrow is at \((-4, 3)\) (since x=-4, y=3), and the right arrow is at \((4, -4)\)? Wait, no, looking at the grid, each square is 1 unit. Let's take two points: (0,0) and (2, -2). So \(y_2 - y_1=-2 - 0=-2\), \(x_2 - x_1=2 - 0=2\), so slope is \(\frac{-2}{2}=-1\). Yes, that's correct. So the slope is -1.

Answer:

\(-1\)