Math Problem Solver

Standard Form:

\[ \begin{aligned}Ax + By + C = 0\end{aligned} \] \[ \begin{aligned} \text{Slope} &= -\frac{A}{B} \\ &= \frac{y_2-y_1}{x_2-x_1} \\ -\frac{A}{B} &= \frac{ -10 - 10 }{ 14 - -11 } \\ -\frac{A}{B} &= \frac{ -20 }{ 25 } \\ A =& 20, B = 25 \end{aligned} \] \[ \begin{aligned} 20 x + 25 y + C &= 0 \\ 20(-11) + 25(10) + C &= 0 \\ + + C &= 0 \\ 250 + C &= 220 \\ C &= 30 \end{aligned} \] An equation of the line in standard form is: \[ 20 x + 25 y - 30 = 0 \]

Slope-Intercept Form:

\[ y = m x + b \] \[ \begin{aligned} \text{Slope} &= \frac{y_2-y_1}{x_2-x_1} \\ \text{Slope} &= \frac{ -10 - 10 }{ 14 - -11 } \\ \text{Slope} &= - \frac{4}{5} \end{aligned} \] \[ \begin{aligned} y &= - \frac{4}{5} x + b \\ 10 &= - \frac{4}{5} \times -11 + b \\ 10 &= \frac{44}{5} + b \\ b &= \frac{6}{5} \end{aligned} \] The slope-intercept form of the line is: \[ y = - \frac{4 x}{5} + \frac{6}{5} \]