Math Problem Solver

Standard Form:

\[ \begin{aligned}Ax + By + C = 0\end{aligned} \] \[ \begin{aligned} \text{Slope} &= -\frac{A}{B} \\ &= \frac{y_2-y_1}{x_2-x_1} \\ -\frac{A}{B} &= \frac{ 4 - 3 }{ 10 - -8 } \\ -\frac{A}{B} &= \frac{ 1 }{ 18 } \\ A =& -1, B = 18 \end{aligned} \] \[ \begin{aligned} -1 x + 18 y + C &= 0 \\ -1(-8) + 18(3) + C &= 0 \\ + + C &= 0 \\ 54 + C &= -8 \\ C &= 62 \end{aligned} \] An equation of the line in standard form is: \[ - x + 18 y - 62 = 0 \]

Slope-Intercept Form:

\[ y = m x + b \] \[ \begin{aligned} \text{Slope} &= \frac{y_2-y_1}{x_2-x_1} \\ \text{Slope} &= \frac{ 4 - 3 }{ 10 - -8 } \\ \text{Slope} &= \frac{1}{18} \end{aligned} \] \[ \begin{aligned} y &= \frac{1}{18} x + b \\ 3 &= \frac{1}{18} \times -8 + b \\ 3 &= - \frac{4}{9} + b \\ b &= \frac{31}{9} \end{aligned} \] The slope-intercept form of the line is: \[ y = \frac{x}{18} + \frac{31}{9} \]