Math Problem Solver

Slope-Intercept Form:

$$\begin{aligned} y = mx+b\end{aligned}$$$$\begin{aligned}y &= - \frac{1}{2}x + b \\ 3 &= - \frac{1}{2} \times 0 + b \\ 3 &= 0 + b \\ b &= 3 \end{aligned}$$An equation of the line in slope-intercept form is: $y = - \frac{x}{2} + 3$

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Point-Slope Form:

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

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Standard Form:

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