Math Problem Solver

Slope-Intercept Form:

$$\begin{aligned} y = mx+b\end{aligned}$$$$\begin{aligned}y &= -3x + b \\ 1 &= -3 \times 2 + b \\ 1 &= -6 + b \\ b &= 7 \end{aligned}$$An equation of the line in slope-intercept form is: $y = - 3 x + 7$

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Point-Slope Form:

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

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Standard Form:

$$\begin{aligned}Ax + By + C = 0\end{aligned}$$$$\begin{aligned} \text{Slope} &= -\frac{A}{B} \\ -\frac{A}{B} &= \frac{-3}{1} \\ A = 3, B = 1 \end{aligned}$$$$\begin{aligned}3 x + 1 y + C &= 0 \\ 3(2) + 1(1) + C &= 0 \\ 6 + 1 + C &= 0 \\ 6 + C &= -1 \\ C &= -7 \end{aligned}$$An equation of the line in standard form is: $3 x + y - 7 = 0$