Math Problem Solver

Standard Form:

\[ \begin{aligned}Ax + By + C = 0\end{aligned} \] \[ \begin{aligned} \text{Slope} &= -\frac{A}{B} \\ &= \frac{y_2-y_1}{x_2-x_1} \\ -\frac{A}{B} &= \frac{ 1 - 2 }{ 3 - 1 } \\ -\frac{A}{B} &= \frac{ -1 }{ 2 } \\ A =& 1, B = 2 \end{aligned} \] \[ \begin{aligned} 1 x + 2 y + C &= 0 \\ 1(1) + 2(2) + C &= 0 \\ + + C &= 0 \\ 4 + C &= -1 \\ C &= 5 \end{aligned} \] An equation of the line in standard form is: \[ x + 2 y - 5 = 0 \]

Slope-Intercept Form:

\[ y = m x + b \] \[ \begin{aligned} \text{Slope} &= \frac{y_2-y_1}{x_2-x_1} \\ \text{Slope} &= \frac{ 1 - 2 }{ 3 - 1 } \\ \text{Slope} &= - \frac{1}{2} \end{aligned} \] \[ \begin{aligned} y &= - \frac{1}{2} x + b \\ 2 &= - \frac{1}{2} \times 1 + b \\ 2 &= - \frac{1}{2} + b \\ b &= \frac{5}{2} \end{aligned} \] The slope-intercept form of the line is: \[ y = - \frac{x}{2} + \frac{5}{2} \]