The slope intercept form is given as y = 1/6x - 3.
To represent a straight line on a graph consider two points namely x and y intercepts of the line. To find x-intercept put y = 0 and for y-intercept put x = 0. Then draw a line passing through these two points.
The given equation is y + 2 = 1/6(x - 6).
It can be written in terms of slope-intercept form y = mx + c as below,
y + 2 = 1/6(x - 6)
=> 6(y + 2) = x - 6
=> 6y + 12 = x - 6
=> 6y = x - 6 - 12
=> y = 1/6(x - 18)
=> y = 1/6x - 3
Hence, slope-intercept form of the given equation is y = 1/6x - 3.
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