# LINR 1 | Lesson 4 | Try This! (Converting between Slope-Intercept and Standard Form ) Solutions

Investigate this idea to develop a process for isolating a variable.

1. Use the equation $$3x-2y=6$$.
• Substitute the value $$x=4$$ into the equation $$3x-2y=6$$.  Isolate the variable $$y$$ by solving the equation for $$y$$.

\begin{align} 3x-2y&=6 \\\\ 3(4)-2y&=6 \\\\ 12-2y&=6 \\\\ 12-12-2y&=6-12 \\\\ -2y&=-6 \\\\ \dfrac{-2y}{-2}&=\dfrac{-6}{-2} \\\\ y&=3\end{align}

• Substitute the value $$x=-6$$ into the equation $$3x-2y=6$$.  Isolate the variable $$y$$ by solving the equation for $$y$$.

\begin{align}3x-2y&=6 \\\\ 3(-6)-2y&=6 \\\\ -18-2y&=6 \\\\ -18+18-2y&=6+18 \\\\ -2y&=24 \\\\ \dfrac{-2y}{-2}&=\dfrac{24}{-2} \\\\y&=-12\end{align}

• Now solve the equation $$3x-2y=6$$ for $$y$$ without knowing a value for $$x$$.  Leave your answer in terms of $$x$$ which means that “$$x$$” will remain in your final equation.

\begin{align} 3x-2y&=6 \\\\ 3x-3x-2y&=6-3x \\\\ -2y&=-3x+6 \\\\ \dfrac{-2y}{-2}&=\dfrac{-3x+6}{-2} \\\\ y&=\dfrac{3}{2}x-3\end{align}

• What is the slope of the line $$3x-2y=6$$?  The slope = $$\dfrac{3}{2}$$
• What is the $$y$$-intercept of the line $$3x-2y=6$$?  The $$y$$-intercept is $$(0,-3)$$

1. Solve the equation $$4x+2y=24$$ for “$$y$$” in terms of “$$x$$” and identify the slope and the $$y$$-intercept.

\begin{align} 4x+2y&=24 \\\\ 4x-4x+2y&=-4x+24 \\\\ \dfrac{2y}{2}&=\dfrac{-4x+24}{2} \\\\ y&=-2x+12\end{align}