Graph:

#2y-6x=10#

You can convert this equation into slope-intercept form by solving for #y#. Slope-intercept form is: #y=mx+b#, where #m# is the slope of the line, and #b# is the y-intercept when #x=0#.

Factor out the common term #2#.

#2(y-3x)=10#

Divide both sides by #2#.

#(2(y-3x))/2=10/2#

Simplify.

#(color(red)cancel(color(black)(2))(y-3x))/color(red)cancel(color(black)(2))=color(red)cancel(color(black)(10^color(blue)5))/color(red)cancel(color(black)(2^color(blue)(1)))#

#y-3x=5#

Add #3x# to both sides.

#y-3x+3x=5+3x#

Simplify.

#y-color(red)cancel(color(black)(3x))+color(red)cancel(color(black)(3x))=5+3x#

#y=3x+5#

The slope is #3# and the y-intercept is #5#. The y-intercept is the point #(0,5)#. The slope is #3/1#. So you can place a point at the y-intercept and move up #3# places and over to the right #1# to get another point. You can also go down #3# places and over to the left #1# place to get another point.

You can also determine ordered pairs using the equation.

#x##color(white)(........)##y#

#0,color(white)(.......)5#

#2,color(white)(.......)11#

#4,color(white)(.......)17#

graph{y=3x+5 [-18.95, 13.1, 1.03, 17.04]}