How do you write an equation of a line containing (2,4) and parallel to #x-2y=5#?

3 Answers
Apr 22, 2018

Answer:

See explanation below
#y#=0.5#x#+3

Explanation:

If a line is parallel to another line it must have the same gradient (co-efficient of #x#)
Re-arrange the given equation of the line into the form #y#=#m##x#+#c#
#x#-2#y#=5
-2#y#=5-#x#
#y#=-2.5+0.5#x#
General equation of line that passes through (2,4)
y=0.5#x#+#c#
Substitute the #x# and #y# coordinate
4=0.5(2)+#c#
4=1+#c#
#c#=3
#y#=0.5#x#+3 (Equation of the parallel line)

I hope this helped

Apr 22, 2018

Answer:

#y=1/2x+3#

Explanation:

#• " Parallel lines have equal slopes"#

#"the equation of a line in "color(blue)"slope-intercept form"# is.

#•color(white)(x)y=mx+b#

#"where m is the slope and b the y-intercept"#

#"rearrange "x-2y=5" into this form"#

#-2y=-x+5#

#"divide all terms by "-2#

#rArry=1/2x-5/2larrcolor(blue)"in slope-intercept form"#

#"with slope m "=1/2#

#rArry=1/2x+blarrcolor(blue)"is the partial equation"#

#"to find b substitute "(2,4)" into the partial equation"#

#4=1+brArrb=4-1=3#

#rArry=1/2x+3larrcolor(red)"equation of parallel line"#

Apr 22, 2018

Answer:

#2y - x = 6#

Explanation:

#x-2y = 5#

#-2y = -x + 5#

#y = (-x/-2) + (5/-2)#

#y = (1/2) x - 5/2#

Slope #m = (1/2)#

Equation of line parallel to given line and passing through (2,4) is

#(y - 4) = (1/2) (x - 2), " using slope - point form"#

#2y - 8 = x - 2#

#2y - x = 6#