Question

Give the slope and y-intercept of the given line.
1.2x-3y=6
2. y=-2x
3. y=3
4. x+2=0

Find the slope of the line that is a) parallel and b) perpendicular to the given line.
1. x=-8
2. y=10

Answer 1

1.


2 x - 3 y = 6

- 3 y = 6 - 2 x Divide both sides by - 3

y = 6 / - 3 - 2 x / - 3

y = - 2 + 2 x / 3

y = ( 2 / 3 ) x - 2


Slope 2 / 3


y - intercept

2 * 0 - 3 y = 6

- 3 y = 6 Divide both sides by - 3

y = 6 / - 3 = - 2


2.


y = - 2 x

Slope - 2


y - intercept


y = - 2 * 0 = 0


3.


y = 3

y = 3 for all value of x

This line is parallel with x axis

Slope = tan 180 ° = 0


y - intercept :

y = 3


4.


x + 2 = 0

x = - 2

x = - 2 for all value of y


This line is parallel with y axis

Slope = tan 90 ° = infinity


y - intercept not exist



1.


x = - 8

x = - 8 for all value of y

This line is parallel with y axis

Slope = tan 90 ° = infinity


a)

Parallel line slope = tan 90 ° = infinity

b)

Normal line slope = tan ( 90 ° - 90 ° ) = tan 0 = 0


2.


y = 10


y = 10 for all value of x

This line is parallel with x axis

Slope = tan 180 ° = 0


a)

Parallel line slope = tan 180 ° = 0
b)

Normal line slope = tan ( 180 ° - 90 ° ) = tan 90 ° = infinity