#color(blue)("Determine "y_("intercept"))#
The y-axis crosses the x-axis at #x=0# so to find the y-intercept substitute #x=0# into the equation
#color(brown)(3x-y=5)color(blue)(" "->" "3(0)-y=5#
But #3xx0=0# giving
#-y=5#
Multiply both sides by #(-1)#
#(-y)xx(-1)=5xx(-1)#
#y=-5#
'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
#color(blue)("Determine "x_("intercept"))#
The x-axis crosses the y-axis at #y=0# so to find the x-intercept substitute #y=0# into the equation
#color(brown)(3x-y=5)color(blue)(" "->" "3x-0=5#
#color(brown)(3x=5)#
Divide both sides by #color(blue)(3)#
#color(brown)(3/(color(blue)(3)) xx x=5/(color(blue)(3))#
But #3/3=1#
#x=5/3#
'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
#color(brown)(3x-y=5)" "->" "color(blue)(y=3x-5)#