Answer:
[tex]y=\dfrac{3}{2}x+6[/tex]
Step-by-step explanation:
Slope-intercept form of a linear equation:
[tex]y=mx+b[/tex]
where:
- m is the slope
- b is the y-intercept
Given equation:
[tex]3x-2y=-12[/tex]
To write the given equation in slope-intercept form, apply arithmetic operations to isolate the variable y.
Add 2y to both sides:
[tex]\implies 3x-2y+2y=-12+2y[/tex]
[tex]\implies 3x=2y-12[/tex]
Add 12 to both sides:
[tex]\implies 3x+12=2y-12+12[/tex]
[tex]\implies 3x+12=2y[/tex]
Switch sides:
[tex]\implies 2y=3x+12[/tex]
Divide both sides by 2:
[tex]\implies \dfrac{2y}{2}=\dfrac{3x+12}{2}[/tex]
[tex]\implies \dfrac{2y}{2}=\dfrac{3x}{2}+\dfrac{12}{2}[/tex]
[tex]\implies y=\dfrac{3}{2}x+6[/tex]
Therefore, the slope-intercept form of the given equation is:
[tex]y=\dfrac{3}{2}x+6[/tex]
where 3/2 is the slope, and 6 is the y-intercept
Learn more about Slope-intercept form here:
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