Math Problem Solver

Standard Form:

$$\begin{aligned}Ax + By + C = 0\end{aligned}$$ $$\begin{aligned} \text{Slope} &= -\frac{A}{B} \\ &= \frac{y_2-y_1}{x_2-x_1} \\ -\frac{A}{B} &= \frac{ 1 - -3 }{ 0 - -3 } \\ -\frac{A}{B} &= \frac{ 4 }{ 3 } \\ A =& -4, B = 3 \end{aligned}$$ $$\begin{aligned} -4 x + 3 y + C &= 0 \\ -4(-3) + 3(-3) + C &= 0 \\ + + C &= 0 \\ 12 + C &= 9 \\ C &= 3 \end{aligned}$$ An equation of the line in standard form is: $$- 4 x + 3 y - 3 = 0$$

Slope-Intercept Form:

$$y = m x + b$$ $$\begin{aligned} \text{Slope} &= \frac{y_2-y_1}{x_2-x_1} \\ \text{Slope} &= \frac{ 1 - -3 }{ 0 - -3 } \\ \text{Slope} &= \frac{4}{3} \end{aligned}$$ $$\begin{aligned} y &= \frac{4}{3} x + b \\ -3 &= \frac{4}{3} \times -3 + b \\ -3 &= -4 + b \\ b &= 1 \end{aligned}$$ The slope-intercept form of the line is: $$y = \frac{4 x}{3} + 1$$