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The line ax + by + c = 0 can be written as y = mx + c, where m is the slope of the line and c is the y-intercept.
6x + 3y - 15 = 0
=> 3y = -6x + 15
=> y = -2x + 5
Therefore the slope is -2.
According to the y=mx+c, "m" symbolize the gradient/slope of the line
therefore y = (-6x+15)/3
y = -2x + 5
Hence slope of the line equals to (-2)
First, we notice that we can divide the entire equation by 3:
2x + y - 5 = 0
Now, we'll put the equation in the slope intercept form:
y = mx + n
m represents the slope and n is the y intercept.
For this reason, we'll move the terms 2x and -5 to the right side of equal sign.
y = -2x + 5
Comparing the forms of equations, we'll conclude that the slope of the given line is m = -2.
The slope of the line y = mx+c is m.
We can convert any line of the form ax+byC= 0 into the form y = mx+c as below:
We subtract ax+c from both sides of ax+by+C = 0:
by = -ax -C.
=> by/b = (-ax-C)/b.
=> y = (-a/b)+(-C/b) which in y = mx+c form.
So -a/b is the slope of ax+by +c = 0.
Therefore in 6x+3y-15 = 0, a= 6, b= 3. So m = -6/3 = -2.
Therefore the slope m of 6x+3y-15 is m = -2.
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