Math Problem Solver

Standard Form:

\[ \begin{aligned}Ax + By + C = 0\end{aligned} \] \[ \begin{aligned} \text{Slope} &= -\frac{A}{B} \\ &= \frac{y_2-y_1}{x_2-x_1} \\ -\frac{A}{B} &= \frac{ 7 - -4 }{ 5 - 2 } \\ -\frac{A}{B} &= \frac{ 11 }{ 3 } \\ A =& -11, B = 3 \end{aligned} \] \[ \begin{aligned} -11 x + 3 y + C &= 0 \\ -11(2) + 3(-4) + C &= 0 \\ + + C &= 0 \\ -12 + C &= 22 \\ C &= -34 \end{aligned} \] An equation of the line in standard form is: \[ - 11 x + 3 y + 34 = 0 \]

Slope-Intercept Form:

\[ y = m x + b \] \[ \begin{aligned} \text{Slope} &= \frac{y_2-y_1}{x_2-x_1} \\ \text{Slope} &= \frac{ 7 - -4 }{ 5 - 2 } \\ \text{Slope} &= \frac{11}{3} \end{aligned} \] \[ \begin{aligned} y &= \frac{11}{3} x + b \\ -4 &= \frac{11}{3} \times 2 + b \\ -4 &= \frac{22}{3} + b \\ b &= - \frac{34}{3} \end{aligned} \] The slope-intercept form of the line is: \[ y = \frac{11 x}{3} - \frac{34}{3} \]