Question

Choose the equation of the line passing through the point (4, -2) and perpendicular to y = one thirdx - 7.

A. y = -3x - 14

B. y = 3x - 10

C. y = -3x + 10

D. y = 3x + 14

Answer 1

y = 1/3x - 7...slope here is 1/3...a perpendicular line will have a negative reciprocal slope. Allll that means is " flip " the slope and change the sign. So the slope we need is -3/1 or just -3....see how I flipped the slope and changed the sign.

y = mx + b
slope(m) = -3
(4,-2)...x = 4 and y = -2
now we sub and find b, the y int
-2 = -3(4) + b
-2 = -12 + b
-2 + 12 = b
10 = b

so ur perpendicular line is : y = -3x + 10

Answer 2

m = -1 / (1/3)
m = -3
The slope-intercept form of the linear equation is:
y = m x + b 
- 2  = - 3 * 4 + b
- 2 = - 12 + b
b = 12 - 2
b = 10
Answer: C ) y = - 3 x + 10