How do you graph #f(x)= 1/4x + 8 # by plotting points?

To pliot a linear function you only need 2 points. So the easiest way to plot a function is to substitute 2 integers to calculate the points.

#f(0)=1/4*0+8=8#

Since there is a denominator #4# it will be easier to substitute #4#

#f(4)=1/4*4+8=1+8=9#

Now we can draw the function.

graph{(y-1/4x-8)(x^2+(y-8)^2-0.5)((x-4)^2+(y-9)^2-0.5)=0 [-32.47, 32.46, -16.23, 16.25]}

The intercepts lie on the line where one of the values is #0#.
That makes it easy to solve for the other value just by looking -- no math necessary.
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The #y# intercept must be the place where #x# equals #0#, which is the ordered pair #(0,y)#

To let #x# equal #0#, just put your fingertip over the #mx# term and hide it.
It would have dropped out to zero anyway.
Then solve the equation in your head.
#f(x)=(1)/(4)x+8#

Cover the #mx# term (which is zero) with your fingertip and solve for #y#
#f(x)=# ░░ #+8#

This gives you the ordered pair #(0,8)#, which is tthe #y# intercept.
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The #x# intercept must be the place where #y# equals #0#, which is the ordered pair #(x,0)#.

To find this point rapidly, cover the #y# term with your fingertip.
It would have ended up as zero anyway.
Then solve for #x# in your head.

░░ #=(1)/(4)x+8#
# - 32 = x#

This gives you the ordered pair #(-32,0)#, which is the #x# intercept.
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Now you have two useful ordered pairs that you can find without doing any math.

#(0,8)# #larr# the #y# intercept
#(-32,0)# #larr# the #x# intercept