Write the equation of the line, with the given properties, in slope-intercept form. slope: -6 and through: (-6,6)

This is very simple. All you need to know is the formula for Point-Slope which is: 
y - y1 = m (x - x1)

The "y" and "x" values are not given, only the "y1", "x1", and slope "m" values are given to us. 

All you need to do is plug in the numbers: 
y - 6 = -6 (x- (-6)         A negative multiplied by a negative is a positive

y - 6 = -6x + 36          Then just add 6 to both sides
y = -6x +30           That's your anwer

However, if they ask you to put it in general form, then simply set everything equal to 0 like so: Ax + By + C = 0 which turns out to be 6x + y - 30 = 0

Point-slope formula;

y - y1 = m(x - x1)        given slope(m) is -6  and the point (-6, 6)

y - 6 = -6(x - (-6)

y - 6 = -6x - 36

y = -6x - 36 + 6

y = -6x - 30   << the equation

hope this helps, God bless!

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