Math Problem Solver

Standard Form:

\[ \begin{aligned}Ax + By + C = 0\end{aligned} \] \[ \begin{aligned} \text{Slope} &= -\frac{A}{B} \\ &= \frac{y_2-y_1}{x_2-x_1} \\ -\frac{A}{B} &= \frac{ 08 - 2 }{ -12 - 28 } \\ -\frac{A}{B} &= \frac{ 6 }{ -40 } \\ A =& -6, B = -40 \end{aligned} \] \[ \begin{aligned} -6 x + -40 y + C &= 0 \\ -6(28) + -40(2) + C &= 0 \\ + + C &= 0 \\ -80 + C &= 168 \\ C &= -248 \end{aligned} \] An equation of the line in standard form is: \[ - 6 x - 40 y + 248 = 0 \]

Slope-Intercept Form:

\[ y = m x + b \] \[ \begin{aligned} \text{Slope} &= \frac{y_2-y_1}{x_2-x_1} \\ \text{Slope} &= \frac{ 08 - 2 }{ -12 - 28 } \\ \text{Slope} &= - \frac{3}{20} \end{aligned} \] \[ \begin{aligned} y &= - \frac{3}{20} x + b \\ 2 &= - \frac{3}{20} \times 28 + b \\ 2 &= - \frac{21}{5} + b \\ b &= \frac{31}{5} \end{aligned} \] The slope-intercept form of the line is: \[ y = - \frac{3 x}{20} + \frac{31}{5} \]