SOLUTION: I need to determine the slope and y intercept of the graph of the linear equation 6x-5y+3=2x-2y-6. In addition to solving can you show me the steps I need to be able to solve like

Question 634163: I need to determine the slope and y intercept of the graph of the linear equation 6x-5y+3=2x-2y-6. In addition to solving can you show me the steps I need to be able to solve like problems? I am not understanding my professor nor is the Math 90 book we are using helping.
Thank You
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
determine the slope and y intercept of the graph of the linear equation 6x-5y+3=2x-2y-6
:
We want this in the slope/intercept form, y = mx + b
:
6x - 5y + 3 = 2x - 2y - 6
subtract 6x from both sides
-5y + 3 = 2x - 6x - 2y - 6
-5y + 3 = -4x - 2y - 6
:
Add 2y to both sides
-5y + 2y + 3 = -4x - 6
-3y + 3 = -4x - 6
:
Subtract 3 from both sides
-3y = -4x - 6 - 3
-3y = -4x - 9
:
y has to be positive, mult both sides by -1
3y = 4x + 9
:
y has to have a coefficient of 1, divide both sides by 3
y = x + 3; this is slope intercept form
therefore
slope (m) =
y intercept occurs when x=0, so y intercept = 3
:
The graph of this

You can see the y axis is intercepted at y=3 and the slope, rises 4 units
for each 3 units horizontally
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