Answer
a) $y=1/2*x+4.5$, Slope-intercept chosen since slope needed to be computed.
b) $y=2x-4$, Slope-intercept chosen since slope and intercept were given.
c) $x+2y = 6$, Standard form chosen since both intercepts were given.
d) $y-2 = -5/3*(x-1)$, Point-slope form chosen since a point and the slope were given
Work Step by Step
a)
$m = (4-2)/(-1--5)$
$m = 2/4 = 1/2$
$y=mx+b$
$2 = -5*1/2 +b$
$2 = -2.5 +b$
$2+2.5 = -2.5 + b + 2.5$
$4.5 = b$
$y=1/2*x+4.5$
b)
$m = 2$, y-intercept = -4
$y=mx+b$
$y=2x-4$
c)
(6,0) and (0,3) are the intercepts
$m = (3-0)/(0-6)$
$m = 3/-6 = -1/2$
$y=mx+b$
$3 = 0*-1/2 +b$
$3 = 0 + b$
$3= b$
$y=-1/2*x+3$
$2*y=2*(-1/2*x+3)$
$2y = -x+6$
$2y+x = -x + 6 +x$
$x+2y = 6$
d)
passes through (1,2) and $m=-5/3$
$y-y_{1} = m*(x-x_{1})$
$y-2 = -5/3*(x-1)$
