SOLUTION: Find the slope and y-intercept 3x+2y=6 can you explain how y=-3/2 (I keep getting y=3/2) where am I going wrong?

Algebra ->  Linear-equations -> SOLUTION: Find the slope and y-intercept 3x+2y=6 can you explain how y=-3/2 (I keep getting y=3/2) where am I going wrong?      Log On


   



Question 178979: Find the slope and y-intercept
3x+2y=6 can you explain how y=-3/2 (I keep getting y=3/2) where am I going wrong?

Answer by solver91311(24713) About Me  (Show Source):
You can put this solution on YOUR website!


To put an equation into slope-intercept form, solve for y:



Add -3x to both sides:





Multiply by





The slope is now the coefficient on x, namely

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Here's another way to look at it, if perhaps you remain unconvinced:

Start with your original equation.



Select a value for x, anything will do so pick something that will make the arithmetic easy, like 1. Substitute this value into the original equation and calculate the value of y:







So now we know that when , , meaning that one of the points on the line is described by the ordered pair .

Repeat the process with another value of x, say 2.







And we have another point on the line: .

Given two points and , the slope can be calculated using:



Substituting our derived coordinates:



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One more idea to carry around with you in your back pocket. Any time you have a 2-variable linear equation written in standard form where the signs on the two variable terms are the same, you will have a negative slope.