How do you find the equation of a line with a slope of 2 and a y intercept of (0,0)?

1 Answer
Dec 31, 2016

Answer:

Use slope-intercept form. See below.

Explanation:

Slope-intercept form is given by #y=mx+b#, where #m# is the slope of the line and #b# is the #y#-intercept of the line, or the value of #y# where the line crosses the #y#-axis.

Given that the slope of the line is #2#, we have #m=2#, and because the line crosses the #y#-axis at the point #(0,0)#, where #y=0# and #x-0#, we have:

#y=2x+0#

Or, equivalently, #y=2x#

If the point given were not the origin, you could use #y=mx+b# to find #b# by plugging the #x# and #y# value of the point in for #x# and #y# in the equation along with the given slope #m# and solving for #b#.

Given #m=2# and #(x,y)=(0,0)#:

#0=2(0)+b#

#=>0=b#

We would then put this value back into #y=mx+b# for #b#, along with the slope #m#, yielding the same answer as above: #y=2x#.