Math Problem Solver

Slope-Intercept Form:

\[\begin{aligned} y = mx+b\end{aligned}\]\[\begin{aligned}\text{Slope} &= \frac{y_2-y_1}{x_2-x_1} \\ \text{Slope} &= \frac{2 - 1}{3 - -3} \\ \text{Slope} &= \frac{1}{6}\end{aligned}\]\[\begin{aligned}y &= \frac{1}{6}x + b \\ 1 &= \frac{1}{6} \times -3 + b \\ 1 &= - \frac{1}{2} + b \\ b &= \frac{3}{2} \end{aligned}\]An equation of the line in slope-intercept form is: $y = \frac{x}{6} + \frac{3}{2}$

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Point-Slope Form:

\[\begin{aligned} y - y_{1} = m(x - x_{1})\end{aligned}\]\[\begin{aligned}\text{Slope} &= \frac{y_2-y_1}{x_2-x_1} \\ \text{Slope} &= \frac{2 - 1}{3 - -3} \\ \text{Slope} &= \frac{1}{6}\end{aligned}\]\[\begin{aligned} y - y_{1} &= m(x - x_{1}) \end{aligned} \\ \] \[ \text{where m } = \frac{1}{6}, \text{ } x_{1} = -3, \text{ and } y_{1} = 1 \]An equation of the line in point-slope form is: $y - 1 = \frac{x + 3}{6}$

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Standard Form:

\[\begin{aligned}Ax + By + C = 0\end{aligned}\]\[\begin{aligned} \text{Slope} &= -\frac{A}{B} \\ \text{Slope} &= \frac{y_2-y_1}{x_2-x_1} \\ -\frac{A}{B} &= \frac{2 - 1}{3 - -3} \\ -\frac{A}{B} &= \frac{1}{6} \\ A = -1, B = 6 \end{aligned}\]\[\begin{aligned}-1x + 6y + C &= 0 \\ -1(-3) + 6(1) + C &= 0 \\ 3 + 6 + C &= 0 \\ 6 + C &= -3 \\ C &= -9 \end{aligned}\]An equation of the line in standard form is: $x - 6 y + 9 = 0$