Math Problem Solver

Slope-Intercept Form:

\[\begin{aligned} y = mx+b\end{aligned}\]\[\begin{aligned}\text{Slope} &= \frac{y_2-y_1}{x_2-x_1} \\ \text{Slope} &= \frac{3 - 0}{0 - -2} \\ \text{Slope} &= \frac{3}{2}\end{aligned}\]\[\begin{aligned}y &= \frac{3}{2}x + b \\ 0 &= \frac{3}{2} \times -2 + b \\ 0 &= -3 + b \\ b &= 3 \end{aligned}\]An equation of the line in slope-intercept form is: $y = \frac{3 x}{2} + 3$

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Point-Slope Form:

\[\begin{aligned} y - y_{1} = m(x - x_{1})\end{aligned}\]\[\begin{aligned}\text{Slope} &= \frac{y_2-y_1}{x_2-x_1} \\ \text{Slope} &= \frac{3 - 0}{0 - -2} \\ \text{Slope} &= \frac{3}{2}\end{aligned}\]\[\begin{aligned} y - y_{1} &= m(x - x_{1}) \end{aligned} \\ \] \[ \text{where m } = \frac{3}{2}, \text{ } x_{1} = -2, \text{ and } y_{1} = 0 \]An equation of the line in point-slope form is: $y = \frac{3 \left(x + 2\right)}{2}$

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Standard Form:

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