Math Problem Solver

Standard Form:

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

Slope-Intercept Form:

\[ y = m x + b \] \[ \begin{aligned} \text{Slope} &= \frac{y_2-y_1}{x_2-x_1} \\ \text{Slope} &= \frac{ 2 - 0 }{ 2 - -1 } \\ \text{Slope} &= \frac{2}{3} \end{aligned} \] \[ \begin{aligned} y &= \frac{2}{3} x + b \\ 0 &= \frac{2}{3} \times -1 + b \\ 0 &= - \frac{2}{3} + b \\ b &= \frac{2}{3} \end{aligned} \] The slope-intercept form of the line is: \[ y = \frac{2 x}{3} + \frac{2}{3} \]