Write in slope intercept form an equation of the line that passes through the given points (-2,,12)

The desired equation is y = x + 8.

Step-by-step explanation:

As we move right from (-2,6) to (4,12), x increases by 6 and y also increases by 6.  Thus, the slope, m, m = rise / run, is m = 6/6, or just m = 1.

Start with the slope intercept form y = mx + b.  Since m = 1, we now have y = x + b.  Subbing 4 for x, 12 for y, we can find b:  12 = 4 + b.  Thus, b = 8.

The desired equation is y = x + 8.