Method 1 : Convert to slope intercept form
#color(white)("XXXX")#A linear equation in the form:
#color(white)("XXXX")##color(white)("XXXX")##y = mx+b#
#color(white)("XXXX")#is in slope intercept form with slope #=m#
#color(white)("XXXX")#and y-intercept #=b#
#3x+4y = 0#
#rarr 4y = -3x + 0#
#rarr y = -3/4x+0##color(white)("XXXX")#(slope intercept form with slope #-3/4# and y intercept #= 0#
Substituting #y=0# into the original equation gives #x=0#, the x-intercept.
Method 2: Use the slope formula for a standard form linear equation
#color(white)("XXXX")#A linear equation in standard form:
#color(white)("XXXX")##color(white)("XXXX")##Ax+By=C#
#color(white)("XXXX")#has a slope of #-(A/B)#
#color(white)("XXXX")#or, in this case
#color(white)("XXXX")##color(white)("XXXX")#-3/4#
The y-intercept is the value of y when #x=0#
#rarr # y intercept # = 0#
The x-intercept is the value of x when #y=0#
#rarr # x intercept # =0#
