Question

(1) find two points on the line.
to move from point to point:
(2) use the tool and draw the δy (the line you move vertically) in blue.
(3) use the tool and draw the δx (the line you move horizontally) in green.
(4) write the slope of the line as a ratio: $\frac{delta y}{delta x}m = _____$
(5) determine if the line has a positive or negative slope.

Explanation:

Step1: Select two points

Selected $(0,3)$ and $(2, - 1)$ from the line.

Step2: Calculate $\Delta y$

$\Delta y=-1 - 3=-4$

Step3: Calculate $\Delta x$

$\Delta x=2 - 0=2$

Step4: Calculate slope

$m=\frac{\Delta y}{\Delta x}=\frac{-4}{2}=-2$

Step5: Determine slope sign

Since $m=-2$, slope is negative.

Answer:

Let's assume two points on the line from the graph: $(0, 3)$ and $(2, - 1)$.

1. Calculate $\Delta y$ and $\Delta x$:

• $\Delta y=y_2 - y_1=-1 - 3=-4$
• $\Delta x=x_2 - x_1=2 - 0 = 2$

1. Calculate the slope $m$:

• $m=\frac{\Delta y}{\Delta x}=\frac{-4}{2}=-2$

1. Determine the sign of the slope:

• Since $m=-2<0$, the slope is negative.

So:

• For (4), $m = - 2$
• For (5), The line has a negative slope.