Math Problem Solver

Slope-Intercept Form:

$$\begin{aligned} y = mx+b\end{aligned}$$$$\begin{aligned}y &= \frac{2}{3}x + b \\ 0 &= \frac{2}{3} \times -6 + b \\ 0 &= -4 + b \\ b &= 4 \end{aligned}$$An equation of the line in slope-intercept form is: $y = \frac{2 x}{3} + 4$

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Point-Slope Form:

$$\begin{aligned} y - y_{1} = m(x - x_{1}) \end{aligned}$$$$ \text{where m } = \frac{2}{3}, \text{ } x_{1} = -6, \text{ and } y_{1} = 0 $$An equation of the line in point-slope form is: $y = \frac{2 \left(x + 6\right)}{3}$

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Standard Form:

$$\begin{aligned}Ax + By + C = 0\end{aligned}$$$$\begin{aligned} \text{Slope} &= -\frac{A}{B} \\ -\frac{A}{B} &= \frac{2}{3} \\ A = -2, B = 3 \end{aligned}$$$$\begin{aligned}-2 x + 3 y + C &= 0 \\ -2(-6) + 3(0) + C &= 0 \\ 12 + 0 + C &= 0 \\ 12 + C &= 0 \\ C &= -12 \end{aligned}$$An equation of the line in standard form is: $2 x - 3 y + 12 = 0$