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= (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= (3+5)/(1)=8`

This is a positive (+) change.

2)


`m= (-4+1)/(2) = (-3)/(2)`

Negative (–).

3)


`m= (-9+4)/(-9+6)= (-5)/(-3)= (5)/(3)`

Positive (+).

4)


`m= (8-3)/(-1+5)= (5)/(4)`

Positive (+).

5)


`m= (4-5)/(2+2)= (-1)/(4)`

Negative (–).