math

write an equation in point-slope form of the line that passes through given point and with the given slope m. (3, -4); m= 6

$\begin{array}{rcr} x_1 &=& 3\\ y_1 &=& -4\\ m&=& 6 \end{array}$

$\begin{array}{rcl} \text{Line: Point Slope Form}\\ \boxed {~ \frac{ y-y_1} {x-x_1} = m ~} \end{array}$

$\begin{array}{rcl} \frac{ y-y_1} {x-x_1} &=& m \\ \frac{ y-(-4)} {x-3} &=& 6 \\ \frac{ y+4} {x-3} &=& 6 \\ y+4 &=& 6\cdot (x-3) \\ y+4 &=& 6\cdot x - 18\\ y &=& 6\cdot x - 18 - 4\\ \mathbf{y} & \mathbf{=} & \mathbf{6\cdot x - 22} \\ \end{array}$