Math Problem Solver

Standard Form:

$$\begin{aligned}Ax + By + C = 0\end{aligned}$$ $$\begin{aligned} \text{Slope} &= -\frac{A}{B} \\ &= \frac{y_2-y_1}{x_2-x_1} \\ -\frac{A}{B} &= \frac{ 5 - 7 }{ -3 - 2 } \\ -\frac{A}{B} &= \frac{ -2 }{ -5 } \\ A =& 2, B = -5 \end{aligned}$$ $$\begin{aligned} 2 x + -5 y + C &= 0 \\ 2(2) + -5(7) + C &= 0 \\ + + C &= 0 \\ 4 + C &= 35 \\ C &= -31 \end{aligned}$$ An equation of the line in standard form is: $$2 x - 5 y + 31 = 0$$

Slope-Intercept Form:

$$y = m x + b$$ $$\begin{aligned} \text{Slope} &= \frac{y_2-y_1}{x_2-x_1} \\ \text{Slope} &= \frac{ 5 - 7 }{ -3 - 2 } \\ \text{Slope} &= \frac{2}{5} \end{aligned}$$ $$\begin{aligned} y &= \frac{2}{5} x + b \\ 7 &= \frac{2}{5} \times 2 + b \\ 7 &= \frac{4}{5} + b \\ b &= \frac{31}{5} \end{aligned}$$ The slope-intercept form of the line is: $$y = \frac{2 x}{5} + \frac{31}{5}$$