Math Problem Solver

Standard Form:

$$\begin{aligned}Ax + By + C = 0\end{aligned}$$ $$\begin{aligned} \text{Slope} &= -\frac{A}{B} \\ &= \frac{y_2-y_1}{x_2-x_1} \\ -\frac{A}{B} &= \frac{ \frac{1}{2} - -1 }{ 1 - \frac{1}{2} } \\ -\frac{A}{B} &= \frac{ \frac{3}{2} }{ \frac{1}{2} } \\ A =& - \frac{3}{2}, B = \frac{1}{2} \end{aligned}$$ $$\begin{aligned} - \frac{3}{2} x + \frac{1}{2} y + C &= 0 \\ - \frac{3}{2}(\frac{1}{2}) + \frac{1}{2}(-1) + C &= 0 \\ + + C &= 0 \\ - \frac{1}{2} + C &= \frac{3}{4} \\ C &= - \frac{5}{4} \end{aligned}$$ An equation of the line in standard form is: $$- 6 x + 2 y + 5 = 0$$

Slope-Intercept Form:

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