Question

D) Find the equations of the lines through YZ

and AB in slope intercept form.
Y(-6,24), z(4,-10), A(-3,-8) and B(-1,2)

Answer 1

A) The equation of line yz passing through point (- 6 , 24) and (4 , -10) is y =
`(-17)/(5)` x +
`(18)/(5)`

B) The equation of line AB passing through point (- 3 , - 8) and (- 1 , 2) is y = 5 x + 7

Explanation:

Given as

A ) The points are

y =
`x_1` ,
`y_1` = - 6 , 24

z =
`x_2` ,
`y_2` = 4 , - 10

Let The slope of line yz = m

So , m =
`(y_2- y_1)/(x_2-x_1)`

Or, m =
`(-10-24)/(4+6)`

Or, m =
`(-17)/(5)`

The equation of the line yz can be written as

y -
`y_1` = m ( x -
`x_1`)

where m is the slope of the line

So, y - 24 = m ( x - (-6))

Or, y - 24 =
`(-17)/(5)` ( x + 6)

Or, 5 ×(y - 24) = -17× (x + 6)

Or, 5 y - 120 = -17 x - 102

Or, 5 y = -17 x -102 + 120

Or, 5 y = -17 x + 18

Or, y =
`(-17)/(5)` x +
`(18)/(5)`

Hence , The equation of line yz passing through point (- 6 , 24) and (4 , -10) is y =
`(-17)/(5)` x +
`(18)/(5)` . Answer

B) The points are

A =
`x_1` ,
`y_1` = - 3 , - 8

B =
`x_2` ,
`y_2` = - 1 , 2

Let The slope of line AB = M

So , M =
`(y_2- y_1)/(x_2-x_1)`

Or, M =
`(2+8)/(-1+3)`

Or, M = 5

The equation of the line yz can be written as

y -
`y_1` = M ( x -
`x_1`)

where m is the slope of the line

So, y - (-8) = M ( x - (-3))

Or, y +8 = 5 ( x + 3)

Or, (y + 8) = 5 × (x + 3)

Or, y + 8 = 5 x + 15

Or, y = 5 x + 15 - 8

Or, y = 5 x + 7

Hence , The equation of line AB passing through point (- 3 , - 8) and (- 1 , 2) is y = 5 x + 7 . Answer