question\ndraw a line representing the \rise\ and a line representing the \run\ of the line. state the slope…

question\ndraw a line representing the \rise\ and a line representing the \run\ of the line. state the slope of the line in simplest form.\nclick twice to plot each segment.\nclick a segment to delete it.

question\ndraw a line representing the \rise\ and a line representing the \run\ of the line. state the slope of the line in simplest form.\nclick twice to plot each segment.\nclick a segment to delete it.

Answer

Explanation:

Step1: Identify two points on the line

Looking at the graph, the line passes through the origin ((0,0)) and another point, say ((1, -2)) (or we can use other points, but let's check the slope formula). Wait, actually, let's take two clear points. Let's see, when (x = 1), (y=-2); when (x = 0), (y = 0).

Step2: Calculate the rise and run

Rise is the change in (y), ( \Delta y=y_2 - y_1). Run is the change in (x), ( \Delta x=x_2 - x_1). Using points ((0,0)) and ((1, -2)), ( \Delta y=-2 - 0=-2), ( \Delta x=1 - 0 = 1).

Step3: Calculate the slope

Slope (m=\frac{\text{rise}}{\text{run}}=\frac{\Delta y}{\Delta x}=\frac{-2}{1}=-2). Wait, maybe another pair. Let's take ((2, -4)) and ((0,0)). Then ( \Delta y=-4-0=-4), ( \Delta x=2 - 0 = 2), so (m=\frac{-4}{2}=-2). So the slope is (-2). Also, to draw rise and run: from a point on the line, go up/down (rise) and left/right (run). For example, from ((0,0)) to ((1, -2)), rise is (-2) (down 2 units) and run is (1) (right 1 unit). So draw a vertical segment (rise) from ((0,0)) down to ((0, -2)) (wait, no, maybe better: from ((1, -2)) to ((1,0)) is rise? Wait, no, rise is vertical change, run is horizontal. Let's correct: for two points ((x_1,y_1)) and ((x_2,y_2)), rise is (y_2 - y_1), run is (x_2 - x_1). So if we take ((0,0)) and ((1, -2)), rise is (-2) (so from ((0,0)) to ((0, -2)) is vertical (rise), then run from ((0, -2)) to ((1, -2)) (horizontal). Wait, no, the rise and run should be between two points. So the correct way: pick a point, say ((0,0)), then move to another point, say ((1, -2)). The vertical change (rise) is (-2) (down 2), horizontal change (run) is (1) (right 1). So draw a vertical line from ((0,0)) down to ((0, -2)) (rise) and a horizontal line from ((0, -2)) to ((1, -2)) (run). Then the slope is rise over run, (\frac{-2}{1}=-2).

Answer:

The slope of the line is (\boxed{-2}) (and for drawing: rise is a vertical segment, run is a horizontal segment as explained).