Math Problem Solver

Standard Form:

\[ \begin{aligned}Ax + By + C = 0\end{aligned} \] \[ \begin{aligned} \text{Slope} &= -\frac{A}{B} \\ &= \frac{y_2-y_1}{x_2-x_1} \\ -\frac{A}{B} &= \frac{ -5 - 4 }{ -1 - 2 } \\ -\frac{A}{B} &= \frac{ -9 }{ -3 } \\ A =& 9, B = -3 \end{aligned} \] \[ \begin{aligned} 9 x + -3 y + C &= 0 \\ 9(2) + -3(4) + C &= 0 \\ + + C &= 0 \\ 18 + C &= 12 \\ C &= 6 \end{aligned} \] An equation of the line in standard form is: \[ 9 x - 3 y - 6 = 0 \]

Slope-Intercept Form:

\[ y = m x + b \] \[ \begin{aligned} \text{Slope} &= \frac{y_2-y_1}{x_2-x_1} \\ \text{Slope} &= \frac{ -5 - 4 }{ -1 - 2 } \\ \text{Slope} &= 3 \end{aligned} \] \[ \begin{aligned} y &= 3 x + b \\ 4 &= 3 \times 2 + b \\ 4 &= 6 + b \\ b &= -2 \end{aligned} \] The slope-intercept form of the line is: \[ y = 3 x - 2 \]