We start by noting that the slope of a line passing through any two points [math]P_1=(x_1, y_1)[/math] and [math]P_2=(x_2, y_2)[/math] can be found as [math]m=\frac{y_2-y_1}{x_2-x_1}[/math]. If we multiply this equation on both sides by [math]x_2-x_1[/math], and switch the sides, we get [math]y_2-y_1=m(x_2-x_1)[/math]. But let's allow [math](x_2, y_2)[/math] to be any point [math](x,y)[/math]. This gives us the [b]point-slope formula[/b] [math]y-y_1=m(x-x_1)[/math]. We can then change this to the slope-intercept form by solving for [math]y[/math]: [math]y=mx+(y_1-mx_1)[/math]. Note that the quantity in the parentheses is "[math]b[/math]", the [math]y[/math]-intercept