Math Problem Solver

Standard Form:

$$\begin{aligned}Ax + By + C = 0\end{aligned}$$ $$\begin{aligned} \text{Slope} &= -\frac{A}{B} \\ &= \frac{y_2-y_1}{x_2-x_1} \\ -\frac{A}{B} &= \frac{ 2 - 3 }{ -\frac{4}{3} - \frac{4}{3} } \\ -\frac{A}{B} &= \frac{ -1 }{ - \frac{8}{3} } \\ A =& 1, B = - \frac{8}{3} \end{aligned}$$ $$\begin{aligned} 1 x + - \frac{8}{3} y + C &= 0 \\ 1(\frac{4}{3}) + - \frac{8}{3}(3) + C &= 0 \\ + + C &= 0 \\ \frac{4}{3} + C &= 8 \\ C &= -8 + \frac{4}{3} \end{aligned}$$ An equation of the line in standard form is: $$3 x - 8 y + 20 = 0$$

Slope-Intercept Form:

$$y = m x + b$$ $$\begin{aligned} \text{Slope} &= \frac{y_2-y_1}{x_2-x_1} \\ \text{Slope} &= \frac{ 2 - 3 }{ -\frac{4}{3} - \frac{4}{3} } \\ \text{Slope} &= \frac{3}{8} \end{aligned}$$ $$\begin{aligned} y &= \frac{3}{8} x + b \\ 3 &= \frac{3}{8} \times \frac{4}{3} + b \\ 3 &= \frac{1}{2} + b \\ b &= \frac{5}{2} \end{aligned}$$ The slope-intercept form of the line is: $$y = \frac{3 x}{8} + \frac{5}{2}$$