Math Problem Solver

Standard Form:

Parallel lines are two lines in the same plane that never intersect. Parallel lines have the same slope, so the slope of the given parallel line can be used to find the slope of the equation.$$\begin{aligned}Ax + By + C &= 0 \\ 2x -3y -7 &= 0 \end{aligned}$$$$\begin{aligned} \text{Slope} &= -\frac{A}{B} \\ \text{Slope} &= \frac{2}{3} \end{aligned}$$ $$\begin{aligned} 2x -3y + C &= 0 \\ 2(1) -3(-2)+C &= 0 \\ 2 +6 + C &= 0 \\ 6 + C &= -2 \\ C &= -8 \end{aligned}$$An equation of the line in standard form is: $2 x - 3 y - 8 = 0$.

Slope-Intercept Form:

Parallel lines are two lines in the same plane that never intersect. Parallel lines have the same slope, so the slope of the given parallel line can be used to find the slope of the equation.$$\begin{aligned} y = mx+b\end{aligned}$$$$\begin{aligned} y &= \frac{2 x}{3} - \frac{7}{3} \\ \text{Slope} &= m = \frac{2}{3} \\ y &= \frac{2}{3}x+b \\ -2 &= \frac{2}{3}(1)+b \\ -2 &= \frac{2}{3} + b \\ b &= - \frac{8}{3} \end{aligned}$$The slope-intercept form of the line is: $y = \frac{2}{3}x - \frac{8}{3}$.