Determine whether y varies directly with x. if so, find the constant of variation and write the equation.

yes; k = 1/4 and y = 1/4x

no

yes; k = 4 and x - 4y

yes; k = 4 and y - 4y

Yes, 4 and  y = 4x

Step-by-step explanation:

By looking at the graphic you see it's a straight line, not a hyperbolic curve, not a logarithm curve either, not a curve at all in fact.  And the line is neither totally horizontal nor totally vertical... so there's a direct relation, a direct positive relation, since the greater the x-value, the greater the y-value.

Then we have to find the constant of variation, or the slope of the line.

We'll take two points on the line (1,4) and (0,0) and examine their variance of Y over their variance of X... that will give us the constant of variation:

So the constant of variation is 4.

Now that we have the slope, its easy to find the full equation:

y = mx + b where m is the slope (we have it) and b is the value for y when x = 0.

By looking at he graph, we see that when x = 0, y = 0 as well.

So, the equation is: y = 4x

where's the diagrams?