Math Problem Solver

Slope-Intercept Form:

$$\begin{aligned} y = mx+b\end{aligned}$$$$\begin{aligned}y &= 6x + b \\ 12 &= 6 \times 10 + b \\ 12 &= 60 + b \\ b &= -48 \end{aligned}$$An equation of the line in slope-intercept form is: $y = 6 x - 48$

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Point-Slope Form:

$$\begin{aligned} y - y_{1} = m(x - x_{1}) \end{aligned}$$$$ \text{where m } = 6, \text{ } x_{1} = 10, \text{ and } y_{1} = 12 $$An equation of the line in point-slope form is: $y - 12 = 6 \left(x - 10\right)$

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Standard Form:

$$\begin{aligned}Ax + By + C = 0\end{aligned}$$$$\begin{aligned} \text{Slope} &= -\frac{A}{B} \\ -\frac{A}{B} &= \frac{6}{1} \\ A = -6, B = 1 \end{aligned}$$$$\begin{aligned}-6 x + 1 y + C &= 0 \\ -6(10) + 1(12) + C &= 0 \\ -60 + 12 + C &= 0 \\ 12 + C &= 60 \\ C &= 48 \end{aligned}$$An equation of the line in standard form is: $6 x - y - 48 = 0$