Question

PLEASE HELP 30 POINTS

Line A is represented by the equation, y=1/4x +5

(a) Write in slope-intercept form the equation of a line that is parallel to Line A and passes through the point, (8, -2). Show your work

(b) Write in slope-intercept form the equation of a line that is perpendicular to Line A and passes through the point, (4,1). Show your work.​

Answer 1

(a) y = 1/4x - 4

(b) y = -4x + 17

Explanation:

Slope-Intercept Form: y = mx + b

m - slope

b - y-intercept

Parallel lines have the same slope but different y-intercepts

Perpendicular lines have the negative reciprocal slope.

Answer 2

(a) y = 1/4x - 4

(b) y = -4x + 17

Explanation:

Slope-Intercept Form: y = mx + b

m - slope

b - y-intercept

(a)

Parallel lines have the same slope but different y-intercepts.

m = 1/4x

y = 1/4x + b

-2 = 1/4(8) + b

-2 = 2 + b

b = -4

y = 1/4x - 4

(b)

Perpendicular lines have the negative reciprocal slope.

m = -4

y = -4x + b

1 = -4(4) + b

1 = -16 + b

b = 17

y = -4x + 17