Math Problem Solver

Standard Form:

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

Slope-Intercept Form:

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