Respuesta :
Answer:
A) The equation of line yz passing through point (- 6 , 24) and (4 , -10) is y = [tex]\frac{-17}{5}[/tex] x + [tex]\frac{18}{5}[/tex]
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 = [tex]x_1[/tex] , [tex]y_1[/tex] = - 6 , 24
z = [tex]x_2[/tex] , [tex]y_2[/tex] = 4 , - 10
Let The slope of line yz = m
So , m = [tex]\dfrac{y_2- y_1}{x_2-x_1}[/tex]
Or, m = [tex]\dfrac{-10-24}{4+6}[/tex]
Or, m = [tex]\frac{-17}{5}[/tex]
The equation of the line yz can be written as
y - [tex]y_1[/tex] = m ( x - [tex]x_1[/tex])
where m is the slope of the line
So, y - 24 = m ( x - (-6))
Or, y - 24 = [tex]\frac{-17}{5}[/tex] ( 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 = [tex]\frac{-17}{5}[/tex] x + [tex]\frac{18}{5}[/tex]
Hence , The equation of line yz passing through point (- 6 , 24) and (4 , -10) is y = [tex]\frac{-17}{5}[/tex] x + [tex]\frac{18}{5}[/tex] . Answer
B) The points are
A = [tex]x_1[/tex] , [tex]y_1[/tex] = - 3 , - 8
B = [tex]x_2[/tex] , [tex]y_2[/tex] = - 1 , 2
Let The slope of line AB = M
So , M = [tex]\dfrac{y_2- y_1}{x_2-x_1}[/tex]
Or, M = [tex]\frac{2+8}{-1+3}[/tex]
Or, M = 5
The equation of the line yz can be written as
y - [tex]y_1[/tex] = M ( x - [tex]x_1[/tex])
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
