Question

Find the slope of the line passing through the pairs of points and describe the line as rising, falling, horizontal or vertical. a. (2 , 1) , (4 , 5) b. (-1 , 0) , (3 , -5) c. (2 , 1) , (-3 , 1) d. (-1 , 2) , (-1 ,- 5)

Answer 1

Answer:

$a.\ m=2,\ \text{the line is rising}\\\\b.\ m=-\dfrac{5}{4},\ \text{the line is falling}\\\\c.\ m=0,\ \text{the line is horizontal}\\\\d.\ m\ is\ unde fined,\ \text{the line is vertical}$

Step-by-step explanation:

The formula of a slope:

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

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

a.

(2, 1) and (4, 5)

$m=\dfrac{5-1}{4-2}=\dfrac{4}{2}=2>0\to\text{rising}$

b.

(-1, 0) and (3, -5)

$m=\dfrac{-5-0}{3-(-1)}=\dfrac{-5}{4}=-\dfrac{5}{4}$

c.

(2, 1) and (-3, 1)

$m=\dfrac{1-1}{-3-2}=\dfrac{0}{-5}=0\to\text{horizontal}$

d.

(-1, 2) and (-1, -5)

$m=\dfrac{-5-2}{-1-(-1))}=\dfrac{-7}{0}\ \text{UNDEFINED}\to\text{vertical}$