What is the slope of the line

Question

-3x+5y=2x+3y

Answer 1

-3x + 5y = 2x + 3y 

 

5y + -3x = 2x + 3y <--- commutative property

 

5y - 3x = 2x + 3y <---  def. of subtraction

 

5y - 3y - 3x = 2x  <--- subtracts 3y from both sides

 

5y - 3y = 3x + 2x <--- adds 3x to both sides

 

2y = 5x  <--- CLT

 

y = (5/2)x  <---- divides both sides by 2

 

THE SLOPE IS (5/2) = (2 and 1/2) = 2.5

 

CHECK:

 

   substitutes y = (5/2)x into the original equation:

 

 left side: -3x + 5(5/2)x = -3x + (25/2)x = (-6/2)x + 25/2 = (19/2)x 

 

right side: 2x + 3(5/2)x = 2x + (15/2)x = (4/2)x + (15/2)x = (19/2)x

 

 

 THE SLOPE IS (5/2) = (2 and 1/2) = 2.5

Answer 2

To find the slope from this form we must put the equation into slope-intercept form(y=mx+b) which involves getting the y variable by itself. So group your x's and y's together (x,y= dummy variables or coordinates on the line. m=slope, b=Y-intercept

 

-3x+5y=2x+3y

+3x-3y=+3x-3y (add 3x to both sides of the equation, and subtract 3y from both sides of the equation)

 

2y=5x (divide both sides by 2)

2    2

 

y=(5/2)x

 

Therefore the slope m=5/2