How to write −6x+2y&lt;42 in slope intercept form?

Question

How to write −6x+2y&amp;lt;42 in slope intercept form?

Ioriannis4v · Accepted Answer

The slope-intercept form of a linear equation is: \(\displaystyle{y}={\color{red}{{m}}}{x}+{\color{blue}{{b}}}\)
Where \(\displaystyle{\color{red}{{m}}}\) is the slope and \(\displaystyle{\color{blue}{{b}}}\) is the y-intercept value.
To isolate the y term and keep the equation balanced, first add \(\displaystyle{\color{red}{{6}{x}}}\) to each side of the inequality:
\(\displaystyle{\color{red}{{6}{x}}}-{6}{x}+{2}{y}{ < }{\color{red}{{6}{x}}}+{42}\)
\(\displaystyle{0}+{2}{y}{ < }{6}{x}+{42}\)
\(\displaystyle{2}{y}{ < }{6}{x}+{42}\)
Now, divide each side of the inequality by \(\displaystyle{\color{red}{{2}}}\) to solve for y and complete the transformation to slope-intercept form while keeping the inequality balanced:
\(\displaystyle\frac{{{2}{y}}}{{\color{red}{{2}}}}{ < }\frac{{{6}{x}+{42}}}{{\color{red}{{2}}}}\)
\(\displaystyle\frac{{{\color{red}{\cancel{{{\color{black}{{2}}}}}}}{y}}}{\cancel{{{\color{red}{{2}}}}}}{ < }\frac{{{6}{x}}}{{\color{red}{{2}}}}+\frac{{42}}{{\color{red}{{2}}}}\)
\(\displaystyle{y}{ < }{\color{red}{{3}}}{x}+{\color{blue}{{21}}}\)

How to write -6x+2y<42 in slope intercept form?

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