Question

PLEASE SOMEONE HELP I NEED IT LIKE RN

1. Write a linear equation with the given information

Through (4,-5), parallel to y = -x + 1(4 Points)

2. Write a linear equation with the given information

Through (2,-1), perpendicular to y = -2/3x + 5(4 Points)

Answer 1

(1)

Parallel Lines admit equal slopes

(D): y=ax+b

(D): y=-x+b

(D) passes through (4,-5)

-5=-(4)+b

b=-5+4=-1

`(d) \: \: y = - x - 1`

(2)

Slopes of 2 perpendicular lines multiply to -1

`a * ( - 2)/(3) = - 1 \\ a = (3)/(2)`

(D): y=(3/2)x+b

Passes through (2,-1)

-1=(3/2)(2)+b

b=-1-3=-4

`(d) \: \: \: \: y = (3)/(2) x - 4`

Answer 2

1. y = -x - 1

2. y = (3/2)x - 4

Explanation:

1. Let y = ax + b be the equation of the line

that passes Through (4,-5) and parallel to y = -x + 1

Where ‘a’ is the slope and b the y value of the y-intercept point.

The lines are parallel

then

they have the same slope

then

a = -1

we get :

y = -x + b and the point (4 , -5) lies on the line

then

-5 = -(4) + b

Then

b = -5 + 4 = -1

Conclusion:

y = -x - 1

………………………………………

2. Let y = mx + p be the equation of the line

that passes Through (2,-1) and perpendicular to y = -2/3x + 5

Where ‘m’ is the slope and p the y value of the y-intercept point.

The lines are perpendicular

then

The product of their slopes = -1

Then

m × (-2/3) = -1

Then

m = 3/2

we get :

y = 3/2x + p and the point (2 , -1) lies on the line

then

-1 = (3/2)×(2) + p

Then

p = -1 - 3 = -4

Conclusion:

y = (3/2)x - 4