Question

3. Line A passes through points (2,4) and (3,6).Write an equation of a line that is parallel to line A.Wrie an equation of a line that will be perpendicular to line A.

Answer 1

@jdoe0001

Answer 2

@jim_thompson5910

Answer 3

@zepdrix

Answer 4

a line parallel to line A will have the same slope as line A
thus, find the slope of line A

then use that, and slap it on an equation in slope-intercept form
with whatever y-intercept you wish

Answer 5

the slope of line a is 2/1 @jdoe0001

Answer 6

yeap is 2/1 or 2

so just slap it on any slope-intercept form
say y - mx + b

m = 2
b = whatever, say hmm 17


so \(\large \bf y = 2x+17\)
it has the same slope as A, thus is parallel

Answer 7

now the perpendicular

well, we know A slope is 2
a line perpendicular to it will have a slope of, NEGATIVE RECIPROCAL
meaning \(\bf slope=\cfrac{2}{{\color{blue}{ 1}}}\qquad negative\implies -\cfrac{2}{{\color{blue}{ 1}}}\qquad reciprocal\implies - \cfrac{{\color{blue}{ 1}}}{2}\)

so now we know the slope of a line perpendicular to A is -1/2
same
slap it on a slope-intercept form
m = -1/2
b = whatever... say hmmm 55

thus \(\large \bf y=-\cfrac{1}{2}x+55\)