Find the set of points that are part of a line that is perpendicular to the line y = ­-3x
a) (-3,-3), (3.-5)
b) (-6,-1), (3,2)
c) (-1, -1), (1, 5)
d) (3, -6), (-1, 6)

the answer is c. (-1, -1), (1, 5)

Step-by-step explanation:

perpindicular lines have reciprocal slopes.

reciprocal terms are two identical numbers, but with opposite signs.

the slope in y= -3x is -3, and the slope in (-1, -1), (1, 5) is 3.

b) (-6,-1), (3,2)

Step-by-step explanation:

We have an equation for a line that is:

where the number is the slope of the line, i will call this number , so

to be a perpendicular line, the slope of the new line must satisfy the following:

and since

so now we check which one of the options is part of a line with  a slope of 1/3, using the formula for the slope:

slope: , this set of points is NOT part of a perpendicular line.

slope:  this set of points are part of a perpendicular line because the slope of the line between them is which is the condition to be a perpendicular line.

b

step-by-step explanation:

the equation of a line in point- slope form is

y - b = m(x - a)

where m is the slope and (a, b) a point on the line

calculate m using the slope formula

m = (y₂ - y₁ ) / (x₂ - x₁ )

with (x₁, y₁ ) = (0, 4) and (x₂, y₂ ) = (3, - 5) ← 2 points on the line

m = = = - 3

with m = - 3 and (a, b) = (3, - 5), then

y - (- 5) = - 3(x - 3), that is

y + 5 = - 3(x - 3) → b