[tex]\text{The point-slope form}\ y-y_1=m(x-x_1)\\\\\text{We have the point}\ \left(\dfrac{1}{2},\ -2\right)\ \text{and}\ m=3.\ \text{Substitute}\\\\y-(-2)=3\left(x-\dfrac{1}{2}\right)\qquad|\text{use distributive property}\\\\y+2=(3)(x)+(3)\left(-\dfrac{1}{2}\right)\\\\y+2=3x-\dfrac{3}{2}\\\\\text{The slope-intercept form:}\ y=mx+b\\\\y+2=3x-1\dfrac{1}{2}\qquad|\text{subtract 2 from both sides}\\\\\boxed{y=3x-3\dfrac{1}{2}}[/tex]
