What are the x and y intercepts of the line described by this equation? 4x-3y=12.3

First of all you need to rearrange the equation to slope-intercept form which is y = mx+b.
so; 4x - 3y = 12.3 will be
 -3y = 12.3 - 4x
rearrange so it will be easy to isolate your y.
-3y = -4x + 12.3
divide both sides by -3
-3y/-3 = -4x/-3 + 12.3/-3
y = 4x/3 - 4.1
so: slope 'm' = 4x/3
      y-intercept = -4.1
      x-intercept = 0

X-intercept is when y=0; 

4x-3(0)=12.3 
4x=12.3 
x=12.3/4 
x=3.075 (x-intercept) 

y-intercept is when x=0 

4(0)-3y=12.3 
-3y=12.3 
y=12.3/-3 
y=-4.1 (y-intercept) 

Hope I helped :)