Math Problem Solver

Standard Form:

$$\begin{aligned}Ax + By + C = 0\end{aligned}$$$$\begin{aligned} \text{Slope} &= -\frac{A}{B} \\ -\frac{A}{B} &= \frac{2}{3} \\ A =& -2, B = 3 \end{aligned}$$$$\begin{aligned}-2 x + 3 y + C &= 0 \\ -2(5) + 3(0) + C &= 0 \\ -10 + 0 + C &= 0 \\ 0 + C &= 10 \\ C &= 10 \end{aligned}$$An equation of the line in standard form is: $- 2 x + 3 y + 10 = 0$.

Slope-Intercept Form:

$$\begin{aligned} y = mx+b\end{aligned}$$$$\begin{aligned}y &= \frac{2}{3}x + b \\ 0 &= \frac{2}{3} \times 5 + b \\ 0 &= \frac{10}{3} + b \\ b &= - \frac{10}{3} \end{aligned}$$The slope-intercept form of the line is: $y = \frac{2 x}{3} - \frac{10}{3}$.