Math Problem Solver

Slope-Intercept Form:

$$\begin{aligned} y = mx+b\end{aligned}$$$$\begin{aligned}y &= \frac{3}{2}x + b \\ 3 &= \frac{3}{2} \times -10 + b \\ 3 &= -15 + b \\ b &= 18 \end{aligned}$$An equation of the line in slope-intercept form is: $y = \frac{3 x}{2} + 18$

---

Point-Slope Form:

$$\begin{aligned} y - y_{1} = m(x - x_{1}) \end{aligned}$$$$ \text{where m } = \frac{3}{2}, \text{ } x_{1} = -10, \text{ and } y_{1} = 3 $$An equation of the line in point-slope form is: $y - 3 = \frac{3 \left(x + 10\right)}{2}$

---

Standard Form:

$$\begin{aligned}Ax + By + C = 0\end{aligned}$$$$\begin{aligned} \text{Slope} &= -\frac{A}{B} \\ -\frac{A}{B} &= \frac{3}{2} \\ A = -3, B = 2 \end{aligned}$$$$\begin{aligned}-3 x + 2 y + C &= 0 \\ -3(-10) + 2(3) + C &= 0 \\ 30 + 6 + C &= 0 \\ 30 + C &= -6 \\ C &= -36 \end{aligned}$$An equation of the line in standard form is: $3 x - 2 y + 36 = 0$