Math Problem Solver

Standard Form:

\[ \begin{aligned}Ax + By + C = 0\end{aligned} \] \[ \begin{aligned} \text{Slope} &= -\frac{A}{B} \\ &= \frac{y_2-y_1}{x_2-x_1} \\ -\frac{A}{B} &= \frac{ -7 - 5 }{ -3 - -9 } \\ -\frac{A}{B} &= \frac{ -12 }{ 6 } \\ A =& 12, B = 6 \end{aligned} \] \[ \begin{aligned} 12 x + 6 y + C &= 0 \\ 12(-9) + 6(5) + C &= 0 \\ + + C &= 0 \\ 30 + C &= 108 \\ C &= -78 \end{aligned} \] An equation of the line in standard form is: \[ 12 x + 6 y + 78 = 0 \]

Slope-Intercept Form:

\[ y = m x + b \] \[ \begin{aligned} \text{Slope} &= \frac{y_2-y_1}{x_2-x_1} \\ \text{Slope} &= \frac{ -7 - 5 }{ -3 - -9 } \\ \text{Slope} &= -2 \end{aligned} \] \[ \begin{aligned} y &= -2 x + b \\ 5 &= -2 \times -9 + b \\ 5 &= 18 + b \\ b &= -13 \end{aligned} \] The slope-intercept form of the line is: \[ y = - 2 x - 13 \]