Answer: [tex]y=4x+3[/tex]
Step-by-step explanation:
By definition the Slope-Intercept form of an equation of a line is:
[tex]y=mx+b[/tex]
Where "m" is the slope of the lines and "b" is the y-intercept.
You have the following equation of the line given in the exercise:
[tex]3y-12x = 9[/tex]
Then, in order to write it in Slope-Intercept form, you need to solve for the variable "y".
The steps are shown below:
1. You must apply the Addition property of Equality adding [tex]12x[/tex] to both sides of the equation:
[tex]3y-12x+12x = 12x+9\\\\3y=12x+9[/tex]
2. Finally, you must apply the Division property of Equality dividing both sides of the equation by 3. Then, you get:
[tex]\frac{3y}{3}=\frac{12x+9}{3}\\\\y=4x+3[/tex]
