Math Problem Solver

Standard Form:

\[ \begin{aligned}Ax + By + C = 0\end{aligned} \] \[ \begin{aligned} \text{Slope} &= -\frac{A}{B} \\ &= \frac{y_2-y_1}{x_2-x_1} \\ -\frac{A}{B} &= \frac{ 3 - 1 }{ -1 - -3 } \\ -\frac{A}{B} &= \frac{ 2 }{ 2 } \\ A =& -2, B = 2 \end{aligned} \] \[ \begin{aligned} -2 x + 2 y + C &= 0 \\ -2(-3) + 2(1) + C &= 0 \\ + + C &= 0 \\ 6 + C &= -2 \\ C &= 8 \end{aligned} \] An equation of the line in standard form is: \[ - 2 x + 2 y - 8 = 0 \]

Slope-Intercept Form:

\[ y = m x + b \] \[ \begin{aligned} \text{Slope} &= \frac{y_2-y_1}{x_2-x_1} \\ \text{Slope} &= \frac{ 3 - 1 }{ -1 - -3 } \\ \text{Slope} &= 1 \end{aligned} \] \[ \begin{aligned} y &= 1 x + b \\ 1 &= 1 \times -3 + b \\ 1 &= -3 + b \\ b &= 4 \end{aligned} \] The slope-intercept form of the line is: \[ y = x + 4 \]