Question 1141345
<pre>
We know that the equation of this graph is y = f(x) = k/x + 3,
and that it passes through the point where the black dot is on the
x-axis which is the point (3/4,0):

{{{drawing(320,400,-4,4,-4,6, 
circle(3/4,0,.16),circle(3/4,0,.13),circle(3/4,0,.1),circle(3/4,0,.075),circle(3/4,0,.05),
graph(320,400,-4,4,-4,6,(-9/4)/x+3),
locate (3/4+.5,.5+.5,(matrix(1,3,3/4,",",0))) )}}}

But we don't know what number k is in this equation:

f(x) = k/x + 3

So we change f(x) to y:

y = k/x + 3

We replace x by the x coordinate of (3/4, 0) which is 3/4 and
we replace y by the y coordinate of (3/4, 0) which is 0:

0 = k/(3/4) + 3

When we divide by a fraction we invert it and multiply:

0 = k∙(4/3) + 3

0 = (4/3)k + 3

We clear the fraction by multiplying through by the denominator 3

 3∙0 = 3∙(4/3)k + 3∙3
   0 = 4k + 9
  -9 = 4k
-9/4 = k

Edwin</pre>