Answer:
[tex]a.\ m=2,\ \text{the line is rising}\\\\b.\ m=-\dfrac{5}{4},\ \text{the line is falling}\\\\c.\ m=0,\ \text{the line is horizontal}\\\\d.\ m\ is\ unde fined,\ \text{the line is vertical}[/tex]
Step-by-step explanation:
The formula of a slope:
[tex]m=\dfrac{y_2-y_1}{x_2-x_1}[/tex]
If
m > 0, then a line is rising
m < 0, then a line is falling
m = 0, then a line is horizontal
m is undefined, then a line is vertical
(2, 1) and (4, 5)
[tex]m=\dfrac{5-1}{4-2}=\dfrac{4}{2}=2>0\to\text{rising}[/tex]
(-1, 0) and (3, -5)
[tex]m=\dfrac{-5-0}{3-(-1)}=\dfrac{-5}{4}=-\dfrac{5}{4}<0\to\text{falling}[/tex]
(2, 1) and (-3, 1)
[tex]m=\dfrac{1-1}{-3-2}=\dfrac{0}{-5}=0\to\text{horizontal}[/tex]
(-1, 2) and (-1, -5)
[tex]m=\dfrac{-5-2}{-1-(-1))}=\dfrac{-7}{0}\ \text{UNDEFINED}\to\text{vertical}[/tex]
