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)

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

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

Step-by-step explanation:

Given as

A ) The points are

y = , = - 6 , 24

z = , = 4 , - 10

Let The slope of line yz = m

So , m =

Or, m =

Or, m =

The equation of the line yz can be written as

y -   = m ( x - )

where m is the slope of the line

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

Or, y - 24 =   ( 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 =   x +

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

B)  The points are

A = , = - 3 , - 8

B = , = - 1 , 2

Let The slope of line AB = M

So , M =

Or, M =

Or, M = 5

The equation of the line yz can be written as

y -   = M ( x - )

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