I am a math student and I remember seeing an equation that graphed literally two parallel lines with one equation. Does anyone have any idea what it may look like?
One equation: Two lines?
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algebra-precalculus
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0$x=\pm k$ for $k>0$? – 2017-02-15
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2Even better: $x^2=k^2$. – 2017-02-15
3 Answers
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Try an equation of the form $(y-mx-c_1)(y-mx-c_2)=0$
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You can get two parallel lines with $|y-x|=1$ or more simply by $|x|=1$. You can get two crossing lines with $(y-x-1)(y+2x+2)=0$
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A general form for the equation of a line is $$ Ax + By + C = 0. $$ Unlike the function graph $y=mx+b,$ this more general form works even if the line is vertical.
To get two lines, just write each line in the form above and multiply the left-hand sides: $$ (A_1x + B_1y + C_1)(A_2x + B_2y + C_2) = 0. $$ To get parallel lines, use the same coefficient for $x$ each time (that is, $A_1 = A_2$) and likewise for $y$ (let $B_1= B_2$), and change only the constant value (let $C_1 \neq C_2$).