We could find the slope with this formula
m = (y₂ - y₁)/(x₂ - x₁)
with (x₁,y₁) and (x₂,y₂) are the points that is located on the line.
NUMBER 20
Given:
(x₁,y₁) = (-2,3)
(x₂,y₂) = (7,-4)
Solution:
Input the points to the formula
m = (y₂ - y₁) / (x₂ - x₁)
m = (-4 - 3) / (7 - (-2))
m = -7 / (7+2)
m = -7/9
The slope of the line is -7/9
NUMBER 21
Given:
(x₁,y₁) = (-6,-1)
(x₂,y₂) = (4,1)
Solution:
Input the points to the formula
m = (y₂ - y₁) / (x₂ - x₁)
m = (1-(-1)) / (4 -(-6))
m = (1+1) / (4+6)
m = 2/10
m = 1/5
The slope of the line is 1/5
NUMBER 22
Given:
(x₁,y₁) = (-9,3)
(x₂,y₂) = (2,1)
Solution:
Input the points to the formula
m = (y₂ - y₁) / (x₂ - x₁)
m = (1 - 3) / (2 - (-9))
m = -2 / (2 + 9)
m = -2/11
The slope of the line is -2/11
Answer:
5 /36
Step-by-step explanation:
Sample space :
Number of faces^number of dice = 6^2 = 36
Sum of 8 on a roll of 2 dies :
Probability = required outcome / Total possible outcomes
Required outcome = number of times a sum of 8 is obtained on a roll of 2 dies = 5
Total possible outcomes = sample space = 36
P(obtaining a sum of 8) = 5 /36
1) gradient of line = Δ y ÷ Δ x
= (5 -2) ÷ (3 - (-6))
= ¹/₃
using the point-slope form (y-y₁) = m(x-x₁)
using (3,5)
(y - 5) = ¹/₃ (x -3)
y - 5 = ¹/₃x - 1
⇒ <span> y = ¹/₃ x + 4 [OPTION D]
</span>2) y = 2x + 5 .... (1)
<span> </span>y = ¹/₂ x + 6 .... (2)
by substituting y in (1) for y in (2)
2x + 5 = ¹/₂ x + 6
³/₂ x = 1
x = ²/₃
by substituting found x (2)
y = ¹/₂ (²/₃) + 6
y = ¹⁹/₃
∴ common point is (²/₃ , ¹⁹/₃) thus answer is FALSE [OPTION B]
3) Yes [OPTION A]
This is because the both have a gradient of 5 and if they have the same gradient then that means that the two lines are parallel to each other.
4) No [OPTION B]
Two lines are perpendicular if their gradients multiply to give - 1 and as such one is the negative reciprocal of the other. Since both gradients are ¹/₂ then they are actually parallel and not perpendicular.
