What is the slope and intercept of #4x+y=1#?

1 Answer
Alan P.
Jun 10, 2016

Slope: #(-4)#
y-intercept#=1color(white)("XXXX")#x-intercept#=1/4#

Explanation:

For a linear equation in the general form:
#color(white)("XXX")color(red)(A)x+color(blue)(B)y=C#
the slope is #m=-color(red)(A)/color(blue)(B)#

For the given equation #color(red)(4)x+y=1rArrcolor(red)(4)x+color(blue)(1)y=1#
this becomes #m=-color(red)(4)/color(blue)(1)#

Alternately, you could convert the equation into slope-intercept form:
#color(white)("XXX")4x+y=1 rArr y=color(green)(-4)x+color(brown)(1)#
with slope #color(green)(-4)# and y-intercept #color(brown)(1)#
The advantage of this method is that it gives you the value of the y-intercept directly (#color(brown)(1)# in this case).

Otherwise the value of the y-intercept is the value of #y# when #x=0#
#color(white)("XXX")4x+y=1# with #x=0#
#color(white)("XXX")rarr 4(0)+y=1#
#color(white)("XXX")rarr y=1#

The x-intercept can be found in a similar manner.
The value of the x-intercept is the value of #x# when #y=0#
#color(white)("XXX")4x+y=1# with #y=0#
#color(white)("XXX")rarr 4x+0=1#
#color(white)("XXX")rarr x=1/4#

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