Math Problem Solver

Standard Form:

$$\begin{aligned}Ax + By + C = 0\end{aligned}$$$$\begin{aligned} \text{Slope} &= -\frac{A}{B} \\ -\frac{A}{B} &= \frac{3}{4} \\ A =& -3, B = 4 \end{aligned}$$$$\begin{aligned}-3 x + 4 y + C &= 0 \\ -3(0) + 4(-6) + C &= 0 \\ 0 + -24 + C &= 0 \\ 0 + C &= 24 \\ C &= 24 \end{aligned}$$An equation of the line in standard form is: $- 3 x + 4 y + 24 = 0$.

Slope-Intercept Form:

$$\begin{aligned} y = mx+b\end{aligned}$$$$\begin{aligned}y &= \frac{3}{4}x + b \\ -6 &= \frac{3}{4} \times 0 + b \\ -6 &= 0 + b \\ b &= -6 \end{aligned}$$The slope-intercept form of the line is: $y = \frac{3 x}{4} - 6$.