Answer:
d. y = -3x -2
Step-by-step explanation:
Given S( 4, 10 ) and T( -2, -8 ) are on a line.
General form of a line is y = ax + b
With :
a = incline or gradient
b = intercept with the y-axis
The gradient can be found by the differences in x-coordinates of S and T divided by differences in y-coordinates of S and T.
a = ( 4 - -2) / (10 - -8)
a = ( 4 + 2) / (10 + 8)
a = 6 / 18
a = 1/3
The question is what is the line which is perpendicular to this line.
General form of a line is y = ax + b
perpendicular to 1/3 = - 3/1 so a = -3
All given lines in answers a, b , c and d have a value for b of -2.
So that line would be y = -3x -2
So the correct answer is d.
Extra:
If you want to find the value of b, of the line through S and T, then you can substitute one of the given points in the line.
y = 1/3x + b
Substitute T(-2, -8)
-8 = (1 * -2)/3 + b
b = -8 + 2/3
the full equation of this line is
y = 1/3x + 8 2/3
y = 1/3x + 8,666666666666666666666
Sometimes written as y = 1/3x + 8,(6)
