Question

Which of the following graphs represent the equation y-4=3(x-1)

Answer 1

First, you should put the equation into the format y = mx + b, like this:

y-4 = 3x-3
y = 3x-3+4 
y = 3x+1

Now we know that the equation intercepts the Y-axis on +1.

This is only true for D; so things point into the direction of D being the right one. To make sure we can try the equation for another point.

Like this:
y = 3*-1 +1
y = -3 + 1 = -2

Which also matches D.

Hence, the correct graph is D. :)

Answer 2

Y-4=3x-3

y=3x+1

Now we don't have the picture but all points must satisfy the y found above.

Of particular note are the x and y intercepts which will be easy to see.

The y intercept is when x=0, so the point (0,1) should be easy to see.  When the line crosses the y axis, y will equal 1.

The x intercept is when y=0, so the point (-1/3, 0) will be where the line crosses the x axis.

These two points will show you which is the correct graph.