SOLUTION: Suppose L1 is the line with equation x - 2y = 6. What is the slope of L1?

Question 652687: Suppose L1 is the line with equation x - 2y = 6. What is the slope of L1?
Found 2 solutions by stanbon, DrBeeee:
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
Suppose L1 is the line with equation x - 2y = 6. What is the slope of L1?
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Solve for "y":
2y = x-6
y = (1/2)x - 3
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slope = 1/2
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Cheers,
Stan H.
Answer by DrBeeee(684) (Show Source): You can put this solution on YOUR website!
To get the slope, rearrange the equation into the following slope-intercept form
(1) y = mx + b
where the coefficient of x is the slope m and b is the known as the y-intercept, i.e. the value of y where the line crosses the y-axis.
You are given the equation for L1 as
(2) x - 2y = 6
Now rearrange the terms to get y all by itself on the left side.
Let's move x to the right side by subtracting x from both sides. It's necessary to perform the SAME arithmetic operation to BOTH side in order to maintain EQUALITY.
(3) x - 2y - x = 6 - x or
(4) - 2y = 6 - x
Now multiple both sides (every term) by (-1)
(5) (-1)(-2y) = (-1)(6) + (-1)*(-x) or
(6) 2y = -6 + x
Let's rewrite (commute) the right side of (6) and get
(7) 2y = x - 6
Now divide both side (every term in the whole equation) by 2 and get
(8) 2y/2 = x/2 - 6/2 or
(9) y = (1/2)x - 3
Now compare each of the 3 terms in (9) to those of (1) and note that
a) The coefficient of y is one in both (1) and (9), a necessary condition,
b) The coefficient of x in (1) is m and in (9) it is 1/2, thus we have
m = 1/2, and
c) the constant term on the right hand side of (1) is b and the constant in (9) is -3, thus we have the y-intercept, b, is equal to -3.
Answer: The line L1 has a slope of 1/2.
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