Math Problem Solver

Standard Form:

\[ \begin{aligned}Ax + By + C = 0\end{aligned} \] \[ \begin{aligned} \text{Slope} &= -\frac{A}{B} \\ &= \frac{y_2-y_1}{x_2-x_1} \\ -\frac{A}{B} &= \frac{ -7 - 6 }{ 5 - 1 } \\ -\frac{A}{B} &= \frac{ -13 }{ 4 } \\ A =& 13, B = 4 \end{aligned} \] \[ \begin{aligned} 13 x + 4 y + C &= 0 \\ 13(1) + 4(6) + C &= 0 \\ + + C &= 0 \\ 24 + C &= -13 \\ C &= 37 \end{aligned} \] An equation of the line in standard form is: \[ 13 x + 4 y - 37 = 0 \]

Slope-Intercept Form:

\[ y = m x + b \] \[ \begin{aligned} \text{Slope} &= \frac{y_2-y_1}{x_2-x_1} \\ \text{Slope} &= \frac{ -7 - 6 }{ 5 - 1 } \\ \text{Slope} &= - \frac{13}{4} \end{aligned} \] \[ \begin{aligned} y &= - \frac{13}{4} x + b \\ 6 &= - \frac{13}{4} \times 1 + b \\ 6 &= - \frac{13}{4} + b \\ b &= \frac{37}{4} \end{aligned} \] The slope-intercept form of the line is: \[ y = - \frac{13 x}{4} + \frac{37}{4} \]