Math Problem Solver

Standard Form:

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

Slope-Intercept Form:

\[ y = m x + b \] \[ \begin{aligned} \text{Slope} &= \frac{y_2-y_1}{x_2-x_1} \\ \text{Slope} &= \frac{ 3 - -3 }{ 2 - -2 } \\ \text{Slope} &= \frac{3}{2} \end{aligned} \] \[ \begin{aligned} y &= \frac{3}{2} x + b \\ -3 &= \frac{3}{2} \times -2 + b \\ -3 &= -3 + b \\ b &= 0 \end{aligned} \] The slope-intercept form of the line is: \[ y = \frac{3 x}{2} \]