The equation of a line is given by:
y = mx + c
where m = slope of line (gradient) and c = the y-intercept (i.e. where the line intercepts the y-axis)
So in your case the slope is -8/5 and the y-intercept is -3
So, m = -8/5 and c = -3
So the equation of the line is:
y = mx + c
y = (-8/5)x + (-3)
y = (-8/5)x - 3
You can then get this in a different form if you want by multiplying both sides of the equation by 5 to get rid of the fraction:
y = (-8/5)x - 3
5y = - 8x - (3x5)
5y = - 8x - 15
You can then add 8x to both sides of the equation to get it in the form you wanted:
5y = - 8x - 15
5y + 8x = - 8x + 8x - 15
5y + 8x = - 15