Math Problem Solver

Standard Form:

\[ \begin{aligned}Ax + By + C = 0\end{aligned} \] \[ \begin{aligned} \text{Slope} &= -\frac{A}{B} \\ &= \frac{y_2-y_1}{x_2-x_1} \\ -\frac{A}{B} &= \frac{ 5 - 2 }{ -6 - 9 } \\ -\frac{A}{B} &= \frac{ 3 }{ -15 } \\ A =& -3, B = -15 \end{aligned} \] \[ \begin{aligned} -3 x + -15 y + C &= 0 \\ -3(9) + -15(2) + C &= 0 \\ + + C &= 0 \\ -27 + C &= 30 \\ C &= -57 \end{aligned} \] An equation of the line in standard form is: \[ - 3 x - 15 y + 57 = 0 \]

Slope-Intercept Form:

\[ y = m x + b \] \[ \begin{aligned} \text{Slope} &= \frac{y_2-y_1}{x_2-x_1} \\ \text{Slope} &= \frac{ 5 - 2 }{ -6 - 9 } \\ \text{Slope} &= - \frac{1}{5} \end{aligned} \] \[ \begin{aligned} y &= - \frac{1}{5} x + b \\ 2 &= - \frac{1}{5} \times 9 + b \\ 2 &= - \frac{9}{5} + b \\ b &= \frac{19}{5} \end{aligned} \] The slope-intercept form of the line is: \[ y = - \frac{x}{5} + \frac{19}{5} \]