Question

Express the equation in slope-intercept form (1/2,-2) and slope m = 3

Answer 1

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