Math Problem Solver

Standard Form:

$$\begin{aligned}Ax + By + C = 0\end{aligned}$$$$\begin{aligned} \text{Slope} &= -\frac{A}{B} \\ -\frac{A}{B} &= \frac{3}{1} \\ A =& -3, B = 1 \end{aligned}$$$$\begin{aligned}-3 x + 1 y + C &= 0 \\ -3(4) + 1(2) + C &= 0 \\ -12 + 2 + C &= 0 \\ 2 + C &= 12 \\ C &= 10 \end{aligned}$$An equation of the line in standard form is: $- 3 x + y + 10 = 0$.

Slope-Intercept Form:

$$\begin{aligned} y = mx+b\end{aligned}$$$$\begin{aligned}y &= 3x + b \\ 2 &= 3 \times 4 + b \\ 2 &= 12 + b \\ b &= -10 \end{aligned}$$The slope-intercept form of the line is: $y = 3 x - 10$.