Systems of linear equations: An equation of a line
The equation of a line
We have seen that solutions of the form #\blue p \cdot x + \green q\cdot y+\purple r=0# have a line as solutions. We have also seen that the linear formula #y = a\cdot x+b# has a line as a graph. Hence, there are two ways of describing the equation of a line.
#y=-{{6\cdot x}\over{7}}+{{5}\over{7}}#
Because the coefficient of #y# is not equal to zero in the given equation, it is possible to reduce the equation to the form #y=a\cdot x+b#. We achieve this form through reduction:
\[\begin{array}{rcl}
6\cdot x+7\cdot y&=&5 \\&&\phantom{xxx}\blue{\text{the given equation}}\\
7\cdot y&=&-6\cdot x+5\\&&\phantom{xxx}\blue{\text{subtracted }6\cdot x\text{ left and right}}\\
y&=&\displaystyle -{{6\cdot x}\over{7}}+{{5}\over{7}}\\&&\phantom{xxx}\blue{\text{left and right divided by the coefficient of }y}
\end{array}\]
Because the coefficient of #y# is not equal to zero in the given equation, it is possible to reduce the equation to the form #y=a\cdot x+b#. We achieve this form through reduction:
\[\begin{array}{rcl}
6\cdot x+7\cdot y&=&5 \\&&\phantom{xxx}\blue{\text{the given equation}}\\
7\cdot y&=&-6\cdot x+5\\&&\phantom{xxx}\blue{\text{subtracted }6\cdot x\text{ left and right}}\\
y&=&\displaystyle -{{6\cdot x}\over{7}}+{{5}\over{7}}\\&&\phantom{xxx}\blue{\text{left and right divided by the coefficient of }y}
\end{array}\]
Unlock full access
Teacher access
Request a demo account. We will help you get started with our digital learning environment.
