Math Problem Solver

Standard Form:

\[ \begin{aligned}Ax + By + C = 0\end{aligned} \] \[ \begin{aligned} \text{Slope} &= -\frac{A}{B} \\ &= \frac{y_2-y_1}{x_2-x_1} \\ -\frac{A}{B} &= \frac{ -9 - -14 }{ 0 - -3 } \\ -\frac{A}{B} &= \frac{ 5 }{ 3 } \\ A =& -5, B = 3 \end{aligned} \] \[ \begin{aligned} -5 x + 3 y + C &= 0 \\ -5(-3) + 3(-14) + C &= 0 \\ + + C &= 0 \\ 15 + C &= 42 \\ C &= -27 \end{aligned} \] An equation of the line in standard form is: \[ - 5 x + 3 y + 27 = 0 \]

Slope-Intercept Form:

\[ y = m x + b \] \[ \begin{aligned} \text{Slope} &= \frac{y_2-y_1}{x_2-x_1} \\ \text{Slope} &= \frac{ -9 - -14 }{ 0 - -3 } \\ \text{Slope} &= \frac{5}{3} \end{aligned} \] \[ \begin{aligned} y &= \frac{5}{3} x + b \\ -14 &= \frac{5}{3} \times -3 + b \\ -14 &= -5 + b \\ b &= -9 \end{aligned} \] The slope-intercept form of the line is: \[ y = \frac{5 x}{3} - 9 \]