Math Problem Solver

Standard Form:

\[ \begin{aligned}Ax + By + C = 0\end{aligned} \] \[ \begin{aligned} \text{Slope} &= -\frac{A}{B} \\ &= \frac{y_2-y_1}{x_2-x_1} \\ -\frac{A}{B} &= \frac{ 2 - 8 }{ 5 - 3 } \\ -\frac{A}{B} &= \frac{ -6 }{ 2 } \\ A =& 6, B = 2 \end{aligned} \] \[ \begin{aligned} 6 x + 2 y + C &= 0 \\ 6(3) + 2(8) + C &= 0 \\ + + C &= 0 \\ 18 + C &= -16 \\ C &= 34 \end{aligned} \] An equation of the line in standard form is: \[ 6 x + 2 y - 34 = 0 \]

Slope-Intercept Form:

\[ y = m x + b \] \[ \begin{aligned} \text{Slope} &= \frac{y_2-y_1}{x_2-x_1} \\ \text{Slope} &= \frac{ 2 - 8 }{ 5 - 3 } \\ \text{Slope} &= -3 \end{aligned} \] \[ \begin{aligned} y &= -3 x + b \\ 8 &= -3 \times 3 + b \\ 8 &= -9 + b \\ b &= 17 \end{aligned} \] The slope-intercept form of the line is: \[ y = - 3 x + 17 \]