Math Problem Solver

Standard Form:

\[ \begin{aligned}Ax + By + C = 0\end{aligned} \] \[ \begin{aligned} \text{Slope} &= -\frac{A}{B} \\ &= \frac{y_2-y_1}{x_2-x_1} \\ -\frac{A}{B} &= \frac{ 8 - 3 }{ -2 - 1 } \\ -\frac{A}{B} &= \frac{ 5 }{ -3 } \\ A =& -5, B = -3 \end{aligned} \] \[ \begin{aligned} -5 x + -3 y + C &= 0 \\ -5(1) + -3(3) + C &= 0 \\ + + C &= 0 \\ -5 + C &= 9 \\ C &= -14 \end{aligned} \] An equation of the line in standard form is: \[ - 5 x - 3 y + 14 = 0 \]

Slope-Intercept Form:

\[ y = m x + b \] \[ \begin{aligned} \text{Slope} &= \frac{y_2-y_1}{x_2-x_1} \\ \text{Slope} &= \frac{ 8 - 3 }{ -2 - 1 } \\ \text{Slope} &= - \frac{5}{3} \end{aligned} \] \[ \begin{aligned} y &= - \frac{5}{3} x + b \\ 3 &= - \frac{5}{3} \times 1 + b \\ 3 &= - \frac{5}{3} + b \\ b &= \frac{14}{3} \end{aligned} \] The slope-intercept form of the line is: \[ y = - \frac{5 x}{3} + \frac{14}{3} \]