We want a line such that it has the point ( 4; -6 ) with the slope m=3/5.
The point slope formula is:
y - y1 = m(x - x1) where (x1,y1) is a point on the line, and m is the slope.
Since we have all these values, we can plug into the formula and get an answer.
y + 6 = .6(x - 4)
We'll have to recall the point slope form of the equation of the line:
y - `y_(1)` = m(x - `x_(1)` )
We'll identify the coordinates `x_(1)` and `y_(1)` as 4 and -6 and we'll replace them, along with the value of the slope, within the equation above:
y - (-6) = (3/5)*(x - 4)
y + 6 = 3x/5 - 12/5
y = 3x/5 - 12/5 - 6
y = 3x/5 - 42/5
The requested equation of the line is y = 3x/5 - 42/5.