# 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 $$y$$.

$3x-2y=6$

$3(4)-2y=6$

$12-2y=6$

$12-12-2y=6-12$

$-2y=-6$

$\frac{-2y}{-2}=\frac{-6}{-2}$

$y=3$

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

$3x-2y=6$

$3(-6)-2y=6$

$-18-2y=6$

$-18+18-2y=6+18$

$-2y=24$

$\frac{-2y}{-2}=\frac{24}{-2}$

$y=-12$

• 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.

$3x-2y=6$

$3x-3x-2y=6-3x$

$-2y=-3x+6$

$\frac{-2y}{-2}=\frac{-3x+6}{-2}$

$y=\frac{3}{2}x-3$

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

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

$4x+2y=24$

$4x-4x+2y=-4x+24$

$\frac{2y}{2}=\frac{-4x+24}{2}$

$y=-2x+12$