Math Problem Solver

Standard Form:

\[ \begin{aligned}Ax + By + C = 0\end{aligned} \] \[ \begin{aligned} \text{Slope} &= -\frac{A}{B} \\ &= \frac{y_2-y_1}{x_2-x_1} \\ -\frac{A}{B} &= \frac{ 8 - -3 }{ -2 - 2 } \\ -\frac{A}{B} &= \frac{ 11 }{ -4 } \\ A =& -11, B = -4 \end{aligned} \] \[ \begin{aligned} -11 x + -4 y + C &= 0 \\ -11(2) + -4(-3) + C &= 0 \\ + + C &= 0 \\ 12 + C &= 22 \\ C &= -10 \end{aligned} \] An equation of the line in standard form is: \[ - 11 x - 4 y + 10 = 0 \]

Slope-Intercept Form:

\[ y = m x + b \] \[ \begin{aligned} \text{Slope} &= \frac{y_2-y_1}{x_2-x_1} \\ \text{Slope} &= \frac{ 8 - -3 }{ -2 - 2 } \\ \text{Slope} &= - \frac{11}{4} \end{aligned} \] \[ \begin{aligned} y &= - \frac{11}{4} x + b \\ -3 &= - \frac{11}{4} \times 2 + b \\ -3 &= - \frac{11}{2} + b \\ b &= \frac{5}{2} \end{aligned} \] The slope-intercept form of the line is: \[ y = - \frac{11 x}{4} + \frac{5}{2} \]