Math Problem Solver

Standard Form:

\[ \begin{aligned}Ax + By + C = 0\end{aligned} \] \[ \begin{aligned} \text{Slope} &= -\frac{A}{B} \\ &= \frac{y_2-y_1}{x_2-x_1} \\ -\frac{A}{B} &= \frac{ 4 - -2 }{ 3 - 2 } \\ -\frac{A}{B} &= \frac{ 6 }{ 1 } \\ A =& -6, B = 1 \end{aligned} \] \[ \begin{aligned} -6 x + 1 y + C &= 0 \\ -6(2) + 1(-2) + C &= 0 \\ + + C &= 0 \\ -2 + C &= 12 \\ C &= -14 \end{aligned} \] An equation of the line in standard form is: \[ - 6 x + y + 14 = 0 \]

Slope-Intercept Form:

\[ y = m x + b \] \[ \begin{aligned} \text{Slope} &= \frac{y_2-y_1}{x_2-x_1} \\ \text{Slope} &= \frac{ 4 - -2 }{ 3 - 2 } \\ \text{Slope} &= 6 \end{aligned} \] \[ \begin{aligned} y &= 6 x + b \\ -2 &= 6 \times 2 + b \\ -2 &= 12 + b \\ b &= -14 \end{aligned} \] The slope-intercept form of the line is: \[ y = 6 x - 14 \]