Question

Find the equation of a line parallel to the line (y+3)=1/2(x-2) and passing through the point (1,5)

Answer 1

paraalell lines have same slope

the equation of a line that passes throug the point (x1,y1) and has a slope of m is
y-y1=m(x-x1)
given
y+3=1/2(x-2)
slope is 1/2 and the point is errelivant

we want to find one that passes through (1,5) and has slope of 1/2

(x1,y1)
(1,5)

y-5=1/2(x-1)
if want standdard or slope intercept
y-5=1/2x-1/2
y=1/2x+9/2

standard
x-2y=-9

Answer 2

parallel lines have the same slope

your given line is in point, slope form

which is


`y - y-{1} = m(x - x_(1))`

so you have


`m = (1)/(2) ~~~~y_(1) = 5~~~~~x_(1) = 1`

just substitute