Math Problem Solver

Standard Form:

\[ \begin{aligned}Ax + By + C = 0\end{aligned} \] \[ \begin{aligned} \text{Slope} &= -\frac{A}{B} \\ &= \frac{y_2-y_1}{x_2-x_1} \\ -\frac{A}{B} &= \frac{ 6 - -2 }{ -20 - -10 } \\ -\frac{A}{B} &= \frac{ 8 }{ -10 } \\ A =& -8, B = -10 \end{aligned} \] \[ \begin{aligned} -8 x + -10 y + C &= 0 \\ -8(-10) + -10(-2) + C &= 0 \\ + + C &= 0 \\ 80 + C &= -20 \\ C &= 100 \end{aligned} \] An equation of the line in standard form is: \[ - 8 x - 10 y - 100 = 0 \]

Slope-Intercept Form:

\[ y = m x + b \] \[ \begin{aligned} \text{Slope} &= \frac{y_2-y_1}{x_2-x_1} \\ \text{Slope} &= \frac{ 6 - -2 }{ -20 - -10 } \\ \text{Slope} &= - \frac{4}{5} \end{aligned} \] \[ \begin{aligned} y &= - \frac{4}{5} x + b \\ -2 &= - \frac{4}{5} \times -10 + b \\ -2 &= 8 + b \\ b &= -10 \end{aligned} \] The slope-intercept form of the line is: \[ y = - \frac{4 x}{5} - 10 \]