Question

1. 18) 19) 20)

Explanation:

Step1: Recall slope formula

The slope formula for a line passing through two points $(x_1,y_1)$ and $(x_2,y_2)$ is $s=\frac{y_2 - y_1}{x_2 - x_1}$.

Step2: For problem 17

Let's assume two points on the line. If we move from one point to another, say we move 2 units to the right (increase in $x$) and 6 units down (decrease in $y$). Then $s=\frac{- 6}{2}=-3$. But if we consider the absolute - value of the ratio of vertical change to horizontal change for the non - negative slope concept used here, if we take the change in $y$ as 6 and change in $x$ as 2, $s = \frac{6}{2}=3$.

Step3: For problem 18

If we move 2 units to the right and 4 units up between two points on the line, then $s=\frac{4}{2}=2$.

Step4: For problem 19

If we move 6 units to the right and 4 units down between two points on the line, then $s=\frac{-4}{6}=-\frac{2}{3}$. Considering the non - negative ratio of vertical to horizontal change as in the given answers, if we take the change in $y$ as 4 and change in $x$ as 6, $s=\frac{4}{6}=\frac{2}{3}$.

Step5: For problem 20

If we move 5 units to the right and 5 units down between two points on the line, then $s=\frac{-5}{5}=-1$. Considering the non - negative ratio of vertical to horizontal change as in the given answers, if we take the change in $y$ as 5 and change in $x$ as 5, $s = \frac{5}{5}=1$.

Answer:

1. $s = 3$
2. $s = 2$
3. $s=\frac{2}{3}$
4. $s = 1$