Math Problem Solver

Standard Form:

\[ \begin{aligned}Ax + By + C = 0\end{aligned} \] \[ \begin{aligned} \text{Slope} &= -\frac{A}{B} \\ &= \frac{y_2-y_1}{x_2-x_1} \\ -\frac{A}{B} &= \frac{ -1 - 1 }{ 4 - 0 } \\ -\frac{A}{B} &= \frac{ -2 }{ 4 } \\ A =& 2, B = 4 \end{aligned} \] \[ \begin{aligned} 2 x + 4 y + C &= 0 \\ 2(0) + 4(1) + C &= 0 \\ + + C &= 0 \\ 4 + C &= 0 \\ C &= 4 \end{aligned} \] An equation of the line in standard form is: \[ 2 x + 4 y - 4 = 0 \]

Slope-Intercept Form:

\[ y = m x + b \] \[ \begin{aligned} \text{Slope} &= \frac{y_2-y_1}{x_2-x_1} \\ \text{Slope} &= \frac{ -1 - 1 }{ 4 - 0 } \\ \text{Slope} &= - \frac{1}{2} \end{aligned} \] \[ \begin{aligned} y &= - \frac{1}{2} x + b \\ 1 &= - \frac{1}{2} \times 0 + b \\ 1 &= 0 + b \\ b &= 1 \end{aligned} \] The slope-intercept form of the line is: \[ y = - \frac{x}{2} + 1 \]