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The slope of the line is determined by the slope-intercept form of the
equation. That is solving for y. or y = mx + b, where m = slope and
b = y-intercept.
The equation 3x + 2y = 6 is written in standard form so we need to
rewrite it in slope - intercept form.
3x + 2y = 6
3x + 2y - 3x = - 3x + 6 --> subtract 3x both sides so to separate 2y
2y = -3x + 6 --> divide both sides by 2 so y will be left
y = -3x + 6
2 2
y = -3x + 3
2
m = -3/2, this is the slope
b = 3, this is the y-intercept