math assignment

Question

(a) Write an equation of the line that passes through the point and is parallel to the given line. (b) Write an equation of the line that passes through the point and is perpendicular to the given line.

Answer 1

for a point (a,c) and line y=mx +b

a parallel line through the point will have the equation

y-c = m(x-a) +b in point slope form

or

y = mx -ma +b+c

where m is the slope and b+c-ma = the y intercept

to take a specific example

y=2x + 2 has a parallel line through the point (0,3)

y = 2x +3

parallel lines have the same slope = the coefficient of the x term when the linear equation is solved for y

a perpendicular line has slope = negative inverse or -1/2 in this example or -1/m more generally where m = slope of the given line

y = -x/2 +3 is the perpendicular line through the point (0,3)