Please show calculations 1 What is the slope of the line th

Please show calculations

1. ) What is the slope of the line that goes through the points (0,7) and ( 5,7) ? And what is the equation of the line .?

b) What is the slope of the line that goes through the points (4,0) and ( 4, - 10) , and also what is the equation of the line ?

2.) a. Two points on a line are ( 0,5) and (8,21) . Determine the slope and y intercept. Write the equation of the line in slope intercept form.

b.) Two points on a line are (0,-6) and (4,4) . Determine the slope and y intercept. Write the equation of the line in slope intercept form.

c.) Two points on a line are (0,7) and (7,0) . Determine the slope and y intercept . Write the equation of the line in slope intercept form

Solution

1 ) a) Given that

( 0,7 ) , ( 5 , 7 )

Let ( x₁ , y₁ ) = ( 0 , 7 )

( x₂ , y₂ ) = ( 5 , 7 )

We know that

Slope m = ( y₂ - y₁ ) / ( x₂ - x₁ )

m = ( 7 - 7 ) / ( 5 - 0 )

= 0 / 5

= 0

Therefore,

Slope m = 0

Thus equation of line is , y - y₁ = m(x - x₁)

Substitute any one point in given points

Let us substitute ( 0 , 7 )

  y - y₁ = m(x - x₁)

  y - 7 = 0(x - 0)

y - 7 = 0

y = 7

Therefore,

The equation of line is , y = 7

b )

Given that

( 4 , 0 ) , ( 4 , -10 )

Let ( x₁ , y₁ ) = ( 4 , 0 )

( x₂ , y₂ ) = ( 4 , -10 )

We know that

Slope m = ( y₂ - y₁ ) / ( x₂ - x₁ )

If x-coordinates are equal then slope is undefined

This means that equation of line does not contain y

Hence,

The equation of line is x = 4

2 ) a )

  Given that

( 0,5 ) , ( 8 ,21 )

Let ( x₁ , y₁ ) = ( 0,5 )

( x₂ , y₂ ) = ( 8 ,21 )

We know that

Slope m = ( y₂ - y₁ ) / ( x₂ - x₁ )

m = ( 21 - 5 ) / ( 8 - 0 )

= 16 / 8

= 2

Therefore,

Slope m = 2

Thus equation of line is , y = mx + b

b = y - mx

b = y - 2.x

Substitute any one point in given points

Let us substitute ( 0 , 5 )

b = y - 2.x

b = 5 - 2.0

b = 5

Hence,

y - intercept = ( 0 , b ) = ( 0 , 5)

Therefore,

The equation of line is , y = mx + b

y = 2x + 5

b )   

Given that

( 0,-6 ) , ( 4 , 4 )

Let ( x₁ , y₁ ) = ( 0,-6 )

( x₂ , y₂ ) =  ( 4 , 4 )

We know that

Slope m = ( y₂ - y₁ ) / ( x₂ - x₁ )

m = ( 4 - (-6) ) / ( 4 - 0 )

= 10 / 4

= 5/2

Therefore,

Slope m = 5/2

Thus equation of line is , y = mx + b

b = y - mx

b = y - (5/2).x

Substitute any one point in given points

Let us substitute ( 0 , -6 )

b = y - (5/2).x

b = -6 - (5/2).0

b = -6

Hence,

y - intercept = ( 0 , b ) = (0 ,-6)

Therefore,

The equation of line is , y = mx + b

y = (5/2)x + (-6)

y = (5/2)x - 6

c )

  Given that

( 0,7 ) , ( 7 , 0 )

Let ( x₁ , y₁ ) = ( 0 , 7 )

( x₂ , y₂ ) =  ( 7 , 0 )

We know that

Slope m = ( y₂ - y₁ ) / ( x₂ - x₁ )

m = ( 0 - 7 ) / ( 7 - 0 )

= -7 / 7

= -1

Therefore,

Slope m = -1

Thus equation of line is , y = mx + b

b = y - mx

b = y - (-1)x

b = y + x

Substitute any one point in given points

Let us substitute ( 0 , 7 )

b = y + x

b = 7 + 0

b = 7

Hence,

y - intercept = ( 0 , b ) = ( 0,7 )

Therefore,

The equation of line is , y = mx + b

y = (-1)x + 7

y = -x + 7