Question

find the slope from the pair of points

1. (2,-5) (1,5) slope = ____ 2) (-5,0) (5,-3) slope = ____

1. (-3,-5) (3,3) slope = ____ 4) (2,4) (-4,-1) slope = ____

1. (-5,1) (5,-1) slope = ____ 6) (3,-5) (5,5) slope = ____

1. (2,1) (3,0) slope = ____ 8) (-5,-2) (5,-1) slope = ____

1. (4,-1) (3,2) slope = ____ 10) (3,-5) (-1,5) slope = ____

Explanation:

Problem 1: $(2, -5)$ and $(1, 5)$

Step 1: Recall the slope formula

The slope \( m \) between two points \( (x_1, y_1) \) and \( (x_2, y_2) \) is given by \( m=\frac{y_2 - y_1}{x_2 - x_1} \). Here, \( x_1 = 2,y_1=-5,x_2 = 1,y_2 = 5 \).

Step 2: Substitute the values into the formula

\( m=\frac{5-(-5)}{1 - 2}=\frac{5 + 5}{-1}=\frac{10}{-1}=- 10 \)

Step 1: Recall the slope formula

The slope \( m \) between two points \( (x_1, y_1) \) and \( (x_2, y_2) \) is given by \( m=\frac{y_2 - y_1}{x_2 - x_1} \). Here, \( x_1=-5,y_1 = 0,x_2=5,y_2=-3 \).

Step 2: Substitute the values into the formula

\( m=\frac{-3-0}{5-(-5)}=\frac{-3}{5 + 5}=\frac{-3}{10}=-\frac{3}{10} \)

Step 1: Recall the slope formula

The slope \( m \) between two points \( (x_1, y_1) \) and \( (x_2, y_2) \) is given by \( m=\frac{y_2 - y_1}{x_2 - x_1} \). Here, \( x_1=-3,y_1=-5,x_2 = 3,y_2=3 \).

Step 2: Substitute the values into the formula

\( m=\frac{3-(-5)}{3-(-3)}=\frac{3 + 5}{3 + 3}=\frac{8}{6}=\frac{4}{3} \)

Answer:

\(-10\)

Problem 2: $(-5, 0)$ and $(5, -3)$