Math Problem Solver

Standard Form:

\[ \begin{aligned}Ax + By + C = 0\end{aligned} \] \[ \begin{aligned} \text{Slope} &= -\frac{A}{B} \\ &= \frac{y_2-y_1}{x_2-x_1} \\ -\frac{A}{B} &= \frac{ -6 - -5 }{ 8 - -10 } \\ -\frac{A}{B} &= \frac{ -1 }{ 18 } \\ A =& 1, B = 18 \end{aligned} \] \[ \begin{aligned} 1 x + 18 y + C &= 0 \\ 1(-10) + 18(-5) + C &= 0 \\ + + C &= 0 \\ -10 + C &= 90 \\ C &= -100 \end{aligned} \] An equation of the line in standard form is: \[ x + 18 y + 100 = 0 \]

Slope-Intercept Form:

\[ y = m x + b \] \[ \begin{aligned} \text{Slope} &= \frac{y_2-y_1}{x_2-x_1} \\ \text{Slope} &= \frac{ -6 - -5 }{ 8 - -10 } \\ \text{Slope} &= - \frac{1}{18} \end{aligned} \] \[ \begin{aligned} y &= - \frac{1}{18} x + b \\ -5 &= - \frac{1}{18} \times -10 + b \\ -5 &= \frac{5}{9} + b \\ b &= - \frac{50}{9} \end{aligned} \] The slope-intercept form of the line is: \[ y = - \frac{x}{18} - \frac{50}{9} \]