Slope-Int: \(y=mx+b\) where \(m\) is slope and \(b\) is y-intercept. Point-Slope: \((y - y_1) = m(x - x_1)\) where \((x_1,y_1)\) is a point on the line and \(m\) is slope. Standard-Form: \(ax+by=c\).
The slope-intercept form of a linear equation shows how steep the line is (slope) and where it crosses the y-axis (intercept). The point-slope form shows that the slope (m) is the change in rise (up the y-axis) over the change in run (along x-axis). In the standard form (also called the general form), the constants \(a\),\(b\) and \(c\) must be integers, \(a\) and \(b\) must be non-zero, and \(a\) must always be positive.
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