Math Problem Solver

Standard Form:

\[ \begin{aligned}Ax + By + C = 0\end{aligned} \] \[ \begin{aligned} \text{Slope} &= -\frac{A}{B} \\ &= \frac{y_2-y_1}{x_2-x_1} \\ -\frac{A}{B} &= \frac{ 12 - 0 }{ 0 - 2 } \\ -\frac{A}{B} &= \frac{ 12 }{ -2 } \\ A =& -12, B = -2 \end{aligned} \] \[ \begin{aligned} -12 x + -2 y + C &= 0 \\ -12(2) + -2(0) + C &= 0 \\ + + C &= 0 \\ 0 + C &= 24 \\ C &= -24 \end{aligned} \] An equation of the line in standard form is: \[ - 12 x - 2 y + 24 = 0 \]

Slope-Intercept Form:

\[ y = m x + b \] \[ \begin{aligned} \text{Slope} &= \frac{y_2-y_1}{x_2-x_1} \\ \text{Slope} &= \frac{ 12 - 0 }{ 0 - 2 } \\ \text{Slope} &= -6 \end{aligned} \] \[ \begin{aligned} y &= -6 x + b \\ 0 &= -6 \times 2 + b \\ 0 &= -12 + b \\ b &= 12 \end{aligned} \] The slope-intercept form of the line is: \[ y = - 6 x + 12 \]