Math Problem Solver

Standard Form:

\[ \begin{aligned}Ax + By + C = 0\end{aligned} \] \[ \begin{aligned} \text{Slope} &= -\frac{A}{B} \\ &= \frac{y_2-y_1}{x_2-x_1} \\ -\frac{A}{B} &= \frac{ -2 - 5 }{ 1 - -5 } \\ -\frac{A}{B} &= \frac{ -7 }{ 6 } \\ A =& 7, B = 6 \end{aligned} \] \[ \begin{aligned} 7 x + 6 y + C &= 0 \\ 7(-5) + 6(5) + C &= 0 \\ + + C &= 0 \\ 30 + C &= 35 \\ C &= -5 \end{aligned} \] An equation of the line in standard form is: \[ 7 x + 6 y + 5 = 0 \]

Slope-Intercept Form:

\[ y = m x + b \] \[ \begin{aligned} \text{Slope} &= \frac{y_2-y_1}{x_2-x_1} \\ \text{Slope} &= \frac{ -2 - 5 }{ 1 - -5 } \\ \text{Slope} &= - \frac{7}{6} \end{aligned} \] \[ \begin{aligned} y &= - \frac{7}{6} x + b \\ 5 &= - \frac{7}{6} \times -5 + b \\ 5 &= \frac{35}{6} + b \\ b &= - \frac{5}{6} \end{aligned} \] The slope-intercept form of the line is: \[ y = - \frac{7 x}{6} - \frac{5}{6} \]