May I please receive help?

Original line: y = -5/6x - 1

A line that is parallel to the original will have the same slope. To find the new y-intercept, we'll take the original line, plug in the given point, and solve for b.

y = -5/6x + b

-2 = -5/6(5) + b

-2 = -25/6 + b

b = 13/6

Parallel Line: y = -5/6x + 13/6

A line that is perpendicular to the original will have the opposite reciprocal slope. To find the new y-intercept, we'll take our perpendicular slope, plug in the given point, and solve for b.

y = 6/5x + b

-2 = 6/5(5) + b

-2 = 6 + b

b = -8

Perpendicular Line: y = 6/5x - 8

Hope this helps!! :)

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