Math Problem Solver

Standard Form:

\[ \begin{aligned}Ax + By + C = 0\end{aligned} \] \[ \begin{aligned} \text{Slope} &= -\frac{A}{B} \\ &= \frac{y_2-y_1}{x_2-x_1} \\ -\frac{A}{B} &= \frac{ 30 - 0 }{ 20 - 0 } \\ -\frac{A}{B} &= \frac{ 30 }{ 20 } \\ A =& -30, B = 20 \end{aligned} \] \[ \begin{aligned} -30 x + 20 y + C &= 0 \\ -30(0) + 20(0) + C &= 0 \\ + + C &= 0 \\ 0 + C &= 0 \\ C &= 0 \end{aligned} \] An equation of the line in standard form is: \[ - 30 x + 20 y = 0 \]

Slope-Intercept Form:

\[ y = m x + b \] \[ \begin{aligned} \text{Slope} &= \frac{y_2-y_1}{x_2-x_1} \\ \text{Slope} &= \frac{ 30 - 0 }{ 20 - 0 } \\ \text{Slope} &= \frac{3}{2} \end{aligned} \] \[ \begin{aligned} y &= \frac{3}{2} x + b \\ 0 &= \frac{3}{2} \times 0 + b \\ 0 &= 0 + b \\ b &= 0 \end{aligned} \] The slope-intercept form of the line is: \[ y = \frac{3 x}{2} \]