3-(3y-2x)/(2)=2x+6 Rewrite in slope-intercept form
3-(3y-2x)/(2)=2x+6
just collect all the y'sn one side:
3 - 3/2 y + x = 2x + 6
-3/2 y = x + 3
y = -2/3 x - 2
To rewrite the equation in slope-intercept form (y = mx + b), we need to isolate the y variable on one side of the equation.
Let's begin by simplifying the equation step by step:
1. Distribute the 3 to the terms in the parentheses:
3 - (3y - 2x)/(2) = 2x + 6
3 - (3y/2 - x) = 2x + 6
2. Remove the parentheses using the distributive property:
3 - 3y/2 + x = 2x + 6
3. Move the x term to the left side of the equation by subtracting x from both sides:
3 - 3y/2 + x - x = 2x - x + 6
3 - 3y/2 = x + 6
4. Move the constant term to the right side of the equation by subtracting 6 from both sides:
3 - 3y/2 - 6 = x + 6 - 6
-3y/2 - 3 = x
5. Simplify the left side of the equation:
-3y/2 - 3 = x
-3y/2 = x + 3
6. Multiply through by -2 to eliminate the fraction:
-3y = 2(x + 3)
7. Divide by -3 to solve for y:
y = (2(x + 3)) / -3
8. Further simplify the equation:
y = -2(x + 3)/3
Now the equation is in slope-intercept form (y = mx + b), where m represents the slope (in this case, -2) and b represents the y-intercept (in this case, -2/3 multiplied by 3).