Math Problem Solver

Standard Form:

\[ \begin{aligned}Ax + By + C = 0\end{aligned} \] \[ \begin{aligned} \text{Slope} &= -\frac{A}{B} \\ &= \frac{y_2-y_1}{x_2-x_1} \\ -\frac{A}{B} &= \frac{ -3 - -2 }{ -4 - 5 } \\ -\frac{A}{B} &= \frac{ -1 }{ -9 } \\ A =& 1, B = -9 \end{aligned} \] \[ \begin{aligned} 1 x + -9 y + C &= 0 \\ 1(5) + -9(-2) + C &= 0 \\ + + C &= 0 \\ 18 + C &= -5 \\ C &= 23 \end{aligned} \] An equation of the line in standard form is: \[ x - 9 y - 23 = 0 \]

Slope-Intercept Form:

\[ y = m x + b \] \[ \begin{aligned} \text{Slope} &= \frac{y_2-y_1}{x_2-x_1} \\ \text{Slope} &= \frac{ -3 - -2 }{ -4 - 5 } \\ \text{Slope} &= \frac{1}{9} \end{aligned} \] \[ \begin{aligned} y &= \frac{1}{9} x + b \\ -2 &= \frac{1}{9} \times 5 + b \\ -2 &= \frac{5}{9} + b \\ b &= - \frac{23}{9} \end{aligned} \] The slope-intercept form of the line is: \[ y = \frac{x}{9} - \frac{23}{9} \]