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

6x+3y-15=0

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.**