Math Problem Solver

Standard Form:

\[ \begin{aligned}Ax + By + C = 0\end{aligned} \] \[ \begin{aligned} \text{Slope} &= -\frac{A}{B} \\ &= \frac{y_2-y_1}{x_2-x_1} \\ -\frac{A}{B} &= \frac{ -5 - -17 }{ 5 - -18 } \\ -\frac{A}{B} &= \frac{ 12 }{ 23 } \\ A =& -12, B = 23 \end{aligned} \] \[ \begin{aligned} -12 x + 23 y + C &= 0 \\ -12(-18) + 23(-17) + C &= 0 \\ + + C &= 0 \\ 216 + C &= 391 \\ C &= -175 \end{aligned} \] An equation of the line in standard form is: \[ - 12 x + 23 y + 175 = 0 \]

Slope-Intercept Form:

\[ y = m x + b \] \[ \begin{aligned} \text{Slope} &= \frac{y_2-y_1}{x_2-x_1} \\ \text{Slope} &= \frac{ -5 - -17 }{ 5 - -18 } \\ \text{Slope} &= \frac{12}{23} \end{aligned} \] \[ \begin{aligned} y &= \frac{12}{23} x + b \\ -17 &= \frac{12}{23} \times -18 + b \\ -17 &= - \frac{216}{23} + b \\ b &= - \frac{175}{23} \end{aligned} \] The slope-intercept form of the line is: \[ y = \frac{12 x}{23} - \frac{175}{23} \]