Question

Anyone know these???

Answer 1

So you correctly wrote that the slope is represented by Δy/Δx. The Greek capital letter delta means "change in," so we are looking at the change in y divided by the change in x. You might also hear this called "rise over run," because change in y is the vertical change (rise) and change in x is the horizontal change (run).

Now, to find the change in y and x, we need to take two points, $(x_1, y_1)$ and $(x_2, y_2)$. We can then find the slope, m, as below:

$m= \dfrac{y_2-y_1}{x_2-x_1}$

So, as we're asked to state the slope and the behavior of the graph. Generally, if you see that as x increases, y increases, then the slope is positive. If y decreases, then the slope is negative. If y stays the same (constant), then the slope is zero. If x is constant, then the slope is undefined. Unfortunately, this worksheet also asks us to calculate the slope. So the equation above comes in handy!

1) let's take x = -1, y = -5 and x = 0, y = 3. We can write $(x_1,y_1)=(-1,-5)$ and $(x_2, y_2)=(0,3)$ (we can choose either point to be $(x_1,y_1)$ so long as we're consistent.

$m= \dfrac{3+5}{1}=8$

This is a positive (+) change.

2) 

$m= \dfrac{-4+1}{2} = \dfrac{-3}{2}$

Negative (–).

3) 

$m= \dfrac{-9+4}{-9+6}= \dfrac{-5}{-3}= \dfrac{5}{3}$

Positive (+).

4)

$m= \dfrac{8-3}{-1+5}= \dfrac{5}{4}$

Positive (+).

5)

$m= \dfrac{4-5}{2+2}= \dfrac{-1}{4}$

Negative (–).