Math Problem Solver

Standard Form:

\[ \begin{aligned}Ax + By + C = 0\end{aligned} \] \[ \begin{aligned} \text{Slope} &= -\frac{A}{B} \\ &= \frac{y_2-y_1}{x_2-x_1} \\ -\frac{A}{B} &= \frac{ 1 - -2 }{ 4 - 1 } \\ -\frac{A}{B} &= \frac{ 3 }{ 3 } \\ A =& -3, B = 3 \end{aligned} \] \[ \begin{aligned} -3 x + 3 y + C &= 0 \\ -3(1) + 3(-2) + C &= 0 \\ + + C &= 0 \\ -3 + C &= 6 \\ C &= -9 \end{aligned} \] An equation of the line in standard form is: \[ - 3 x + 3 y + 9 = 0 \]

Slope-Intercept Form:

\[ y = m x + b \] \[ \begin{aligned} \text{Slope} &= \frac{y_2-y_1}{x_2-x_1} \\ \text{Slope} &= \frac{ 1 - -2 }{ 4 - 1 } \\ \text{Slope} &= 1 \end{aligned} \] \[ \begin{aligned} y &= 1 x + b \\ -2 &= 1 \times 1 + b \\ -2 &= 1 + b \\ b &= -3 \end{aligned} \] The slope-intercept form of the line is: \[ y = x - 3 \]