Question

finding the slope graphically
question
draw a line representing the
ise\ and a line representing the
un\ of the line. state the slope of the line in simplest form.
click twice to plot each segment.
click a segment to delete it.
answer

Explanation:

Step1: Identify two points on the line

Looking at the graph, let's take two clear points. Let's assume the line passes through \((0, 2)\) and \((1, -1)\) (we can check the grid, but for slope calculation, we need two points). Wait, maybe better to find the rise and run. Let's pick two points: let's say when \(x = 0\), \(y = 2\) (y-intercept) and when \(x = 1\), \(y=-1\)? Wait, no, maybe another pair. Wait, the line is decreasing, so slope is negative. Let's take two points: let's say \((0, 2)\) and \((2, -4)\)? Wait, maybe the correct way is to find the change in y (rise) and change in x (run). Let's take two points on the line. Let's say the line passes through \((0, 2)\) and \((1, -1)\)? Wait, no, let's check the grid. Wait, maybe the two points are \((0, 2)\) and \((2, -4)\)? Wait, no, let's do it properly. Let's take two points: let's say \((0, 2)\) and \((1, -1)\)? Wait, no, the slope formula is \(m=\frac{y_2 - y_1}{x_2 - x_1}\). Let's pick two points: let's say \((0, 2)\) and \((2, -4)\). Then \(y_2 - y_1=-4 - 2=-6\), \(x_2 - x_1=2 - 0 = 2\). Wait, no, that gives slope \(\frac{-6}{2}=-3\). Wait, maybe another pair. Wait, maybe the line goes through \((0, 2)\) and \((1, -1)\): \(y_2 - y_1=-1 - 2=-3\), \(x_2 - x_1=1 - 0 = 1\), so slope is \(-3\). Wait, let's check the graph again. Let's see, from the y-intercept (0,2), if we move 1 unit to the right (run = 1), we move down 3 units (rise = -3). So rise over run is \(\frac{-3}{1}=-3\). So the slope is -3.

Step2: Calculate the slope

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

Answer:

The slope of the line is \(-3\).