Math Problem Solver

Standard Form:

\[ \begin{aligned}Ax + By + C = 0\end{aligned} \] \[ \begin{aligned} \text{Slope} &= -\frac{A}{B} \\ &= \frac{y_2-y_1}{x_2-x_1} \\ -\frac{A}{B} &= \frac{ -1 - 4 }{ 6 - 1 } \\ -\frac{A}{B} &= \frac{ -5 }{ 5 } \\ A =& 5, B = 5 \end{aligned} \] \[ \begin{aligned} 5 x + 5 y + C &= 0 \\ 5(1) + 5(4) + C &= 0 \\ + + C &= 0 \\ 20 + C &= -5 \\ C &= 25 \end{aligned} \] An equation of the line in standard form is: \[ 5 x + 5 y - 25 = 0 \]

Slope-Intercept Form:

\[ y = m x + b \] \[ \begin{aligned} \text{Slope} &= \frac{y_2-y_1}{x_2-x_1} \\ \text{Slope} &= \frac{ -1 - 4 }{ 6 - 1 } \\ \text{Slope} &= -1 \end{aligned} \] \[ \begin{aligned} y &= -1 x + b \\ 4 &= -1 \times 1 + b \\ 4 &= -1 + b \\ b &= 5 \end{aligned} \] The slope-intercept form of the line is: \[ y = - x + 5 \]