Math Problem Solver

Standard Form:

\[ \begin{aligned}Ax + By + C = 0\end{aligned} \] \[ \begin{aligned} \text{Slope} &= -\frac{A}{B} \\ &= \frac{y_2-y_1}{x_2-x_1} \\ -\frac{A}{B} &= \frac{ 5 - 2 }{ 19 - -1 } \\ -\frac{A}{B} &= \frac{ 3 }{ 20 } \\ A =& -3, B = 20 \end{aligned} \] \[ \begin{aligned} -3 x + 20 y + C &= 0 \\ -3(-1) + 20(2) + C &= 0 \\ + + C &= 0 \\ 40 + C &= -3 \\ C &= 43 \end{aligned} \] An equation of the line in standard form is: \[ - 3 x + 20 y - 43 = 0 \]

Slope-Intercept Form:

\[ y = m x + b \] \[ \begin{aligned} \text{Slope} &= \frac{y_2-y_1}{x_2-x_1} \\ \text{Slope} &= \frac{ 5 - 2 }{ 19 - -1 } \\ \text{Slope} &= \frac{3}{20} \end{aligned} \] \[ \begin{aligned} y &= \frac{3}{20} x + b \\ 2 &= \frac{3}{20} \times -1 + b \\ 2 &= - \frac{3}{20} + b \\ b &= \frac{43}{20} \end{aligned} \] The slope-intercept form of the line is: \[ y = \frac{3 x}{20} + \frac{43}{20} \]