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.
1) -3(5x+2y=-3)⇒ -15x-6y=9
⇒ -9x=27
2(3x+3y=9)⇒ 6x+6y=18
2) -9x/-9=27/-9 ⇒ x=-3
3) 3(-3)+3y=9⇒ -9+9+3y=9+9⇒ 3y/3=18/3⇒ y=6
Answer: (-3,6)
Reasoning:
Step 1) In order to eliminate, first I had to multiple the first equation by -3 and the second by 2 so that when combining the equations y would cancel each other out so that I could solve for x. <em>Note: There are many combinations as to how you could multiple the equations so that either the x or y would cancel out.
</em>
Step 2) Once y is eliminated, solve for x.
Step 3) Now plug x back into one of the original equations and solve for y. <em>Note: Plug x back into one of the original equations, not the equations that were changed by multiplication,</em>
Answer:
a1 = 6 and an = an-1 - 5
a2 = a2-1 - 5 = a1 - 5 = 1
a3 = a3-1 - 5 = a2 - 5 = -4, etc
Step-by-step explanation:
Answer:
the study in which observations are made, experiments are done and logical conclusions are drawn in order to understand the principles of nature.
