Question

Need help.

Answer 1

Answer:

1. y= 3x+7

2.y=1/2 x -1

Step-by-step explanation:

1.

Parallel lines have the same gradient.In the equation given,

y= 3x+5 , the slope is 3

So now, you find the equation of a line passing through point (-1,4) with m=3

m=Δ y/Δx

3= y-4/ x--1

3= y-4 /x+1

3(x+1) = y-4

3x+3 =y-4

3x+3+4=y

⇒⇒ y= 3x+7   is the equation.

2.

Two lines that are perpendicular to each other have the product of their slopes to be -1

Given equation to be y= -2x +8 then, m₁ = -2

Finding m₂ will be;

m₁ *m₂ = -1

-2 * m₂ = -1

-2 m₂ = -1

m₂ = -1/-2 = 1/2

So writing the equation of the perpendicular line with m₂ =1/2 , point (-4,-3)

will be;

m=Δy/Δx

1/2=y--3/x--4

1/2 = y+3/x+4

x+4 = 2( y+3)

x+4 = 2(y+3)

x+4 =2y+6

x+4-6=2y

x-2=2y

x/2 -2/2=y

y=1/2 x -1   is the equation.