Which shows the equation of the line containing the points (-2, 6) and having a slope of 3 in intercept-form?

We know that the slope-intercept form of an equation is represented by:

y = mx + b

Where m is the slope, b is the y-intercept, and x and y pertain to points on the line in the graph.

So the slope of the line is know to be 3, and we are able to plug that into the equation:

y = 3x + b

We also know that the point (-2, 6) is on the line. With this information, we can then plug in the point into the equation to find b:

6 = 3(-2) + b

Then we can solve for b:

6 = -6 + b

b = 12

Knowing that b is 12, we can then rewrite the equation in a more general slope-intercept form that is applicable to any point on that line:

y = 3x + 12

Thus, your answer would be C.