Step 1. Solve the equation for #y# in terms of #x#.
Subtract #7x# from both sides
#7xcolor(red)(-7x)+8y=29color(red)(-7x)#
#8y=29-7x#
Divide both sides by #8#
#(cancel(8)y)/color(red)(cancel(8))=(29-7x)/color(red)(8)#
#y=29/8-7/8x" "# or #" " y=-7/8x+29/8#
Step 2. Solve for important parts of the line.
#y#-intercept: Let #x=0#
#y=-7/8xxcolor(red)(0)+29/8#
#y=0+29/8=29/8~~3.625#
So the #y#-intercept is #(0,3.625)#
#x#-intercept: Let #y=0#
#color(red)(0)=-7/8x+29/8#
Multiply all sides by #8# to get rid of the ugly fractions.
#color(red)(8)xx0=color(red)(8)xx(-7/8)x+color(red)(8)xx(29/8)#
#0=-7x+29#
Add #7x# to both sides
#7x=29#
Divide both sides by #7#
#x=29/7~~4.14#
So the #x#-intercept is #(4.14,0)#
Step 3. Plot these two intercepts and draw a line connecting them
