Geometry: Lines
Different descriptions of a line
We have already seen that the equation of a line is uniquely determined by two distinct points on the line. We have also seen that the graph of a linear function is a straight line and we described two different ways of writing the equation of a line. We will recall these different descriptions and add a third equation for a line.
#y=4\cdot x+{{10}\over{3}}#
Because the coefficient of #y# in the given equation is not equal to zero, it's posible to rewrite the equation as #y=a\cdot x+b#. We get to this form using reduction:
\[\begin{array}{rcl}
3\cdot x-{{3}\over{4}}\cdot y&=&-{{5}\over{2}}\\&&\phantom{xxx}\blue{\text{the given equation}}\\
-{{3}\over{4}}\cdot y&=&-3\cdot x-{{5}\over{2}}\\&&\phantom{xxx}\blue{3\cdot x\text{ subtracted}\text{ on both sides}}\\
y&=&4\cdot x+{{10}\over{3}}\\&&\phantom{xxx}\blue{\text{left and right hand side divided by } -{{3}\over{4}} \text{, the coeffient of } y}
\end{array}\]
Because the coefficient of #y# in the given equation is not equal to zero, it's posible to rewrite the equation as #y=a\cdot x+b#. We get to this form using reduction:
\[\begin{array}{rcl}
3\cdot x-{{3}\over{4}}\cdot y&=&-{{5}\over{2}}\\&&\phantom{xxx}\blue{\text{the given equation}}\\
-{{3}\over{4}}\cdot y&=&-3\cdot x-{{5}\over{2}}\\&&\phantom{xxx}\blue{3\cdot x\text{ subtracted}\text{ on both sides}}\\
y&=&4\cdot x+{{10}\over{3}}\\&&\phantom{xxx}\blue{\text{left and right hand side divided by } -{{3}\over{4}} \text{, the coeffient of } y}
\end{array}\]
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