How do you graph using the intercepts for #2x-4y=42#?

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Answer 1 · 2018-05-10T07:33:14

#x#-intercept: #(21,0)#
#y#-intercept: #(0,-\frac{21}{2})#

Be definition, a coordinate axis is defined as the sets of points where the other coordinate is zero, i.e.:

#x#-axis: #{(x,y) \in \mathbb{R}^2 : y = 0}#

#y#-axis: #{(x,y) \in \mathbb{R}^2 : x = 0}#

So, the line intercepts the #x#-axis where #y=0#, i.e.

#2x-4\cdot 0 = 42 \iff 2x = 42 \iff x = 21#

So, the point is #(21,0)#

As for the #y#-axis, we must impose #x=0#:

#2\cdot 0 - 4y=42 \iff - 4y=42 \iff y = -\frac{42}{4} = -\frac{21}{2} #

So, the point is #(0,-\frac{21}{2})#