Who's Right?
Directions:
1. Read the question below.
2. Answer each part the question in the discussion posted in Schoology.
Michaela was trying to determine the slope of the line shown at right, so she selected two points where the grid
lines intersect and then drew a slope triangle.
a. Her teammate, Cynthia, believes that the change in the vertical
distance is 3, shown as Ay = 3, because the triangle is three units
tall, while her other teammate, Essie, thinks that the change in
the vertical distance is 3, shown as Ay = -3, because the triangle
is three units tall and the line is pointing downward from left to
right. With whom do you agree and why?
b. After settling the first disagreement, Michaela noticed the
following. Michaela noticed that Cynthia wrote 4 on her paper
_ 3
for the slope of the line, while Essie wrote 4 on her paper for
the slope of the line. Michaela asked the group, "Are these ratios
equal?" What did the group answer? Justify your response.
1 2 3 4 5 6 7 8 9
X

The slope is negative. Intuitively, you can see that as x increases (i.e. we move to the right), y decreases (i.e. we move downwards). Using formulas, you can see that the two highlighted points are (4,6) and (8,3). The formula for the slope is

[tex]m=\dfrac{\Delta y}{\Delta x}=\dfrac{y_2-y_1}{x_2-x_1}=\dfrac{3-6}{8-4}=\dfrac{-3}{4}[/tex]

So, in particular, you can see that we have

[tex]\Delta y=-3,\quad \Delta x=4[/tex]

As for the second questions, the writings

[tex]\dfrac{-3}{4},\quad \dfrac{3}{-4},\quad -\dfrac{3}{4}[/tex]

are perfectly equivalent. In fact, 3/4 will always be 0.75, and the rules for the sign tells you that:

positive/negative=negative

negative/positive=negative

-(positive/positive)=-(positive)=negative