Math Problem Solver

Standard Form:

\[ \begin{aligned}Ax + By + C = 0\end{aligned} \] \[ \begin{aligned} \text{Slope} &= -\frac{A}{B} \\ &= \frac{y_2-y_1}{x_2-x_1} \\ -\frac{A}{B} &= \frac{ 6 - -2 }{ 3 - 1 } \\ -\frac{A}{B} &= \frac{ 8 }{ 2 } \\ A =& -8, B = 2 \end{aligned} \] \[ \begin{aligned} -8 x + 2 y + C &= 0 \\ -8(1) + 2(-2) + C &= 0 \\ + + C &= 0 \\ -4 + C &= 8 \\ C &= -12 \end{aligned} \] An equation of the line in standard form is: \[ - 8 x + 2 y + 12 = 0 \]

Slope-Intercept Form:

\[ y = m x + b \] \[ \begin{aligned} \text{Slope} &= \frac{y_2-y_1}{x_2-x_1} \\ \text{Slope} &= \frac{ 6 - -2 }{ 3 - 1 } \\ \text{Slope} &= 4 \end{aligned} \] \[ \begin{aligned} y &= 4 x + b \\ -2 &= 4 \times 1 + b \\ -2 &= 4 + b \\ b &= -6 \end{aligned} \] The slope-intercept form of the line is: \[ y = 4 x - 6 \]