Math Problem Solver

Standard Form:

\[ \begin{aligned}Ax + By + C = 0\end{aligned} \] \[ \begin{aligned} \text{Slope} &= -\frac{A}{B} \\ &= \frac{y_2-y_1}{x_2-x_1} \\ -\frac{A}{B} &= \frac{ 2 - 7 }{ 6 - 5 } \\ -\frac{A}{B} &= \frac{ -5 }{ 1 } \\ A =& 5, B = 1 \end{aligned} \] \[ \begin{aligned} 5 x + 1 y + C &= 0 \\ 5(5) + 1(7) + C &= 0 \\ + + C &= 0 \\ 25 + C &= -7 \\ C &= 32 \end{aligned} \] An equation of the line in standard form is: \[ 5 x + y - 32 = 0 \]

Slope-Intercept Form:

\[ y = m x + b \] \[ \begin{aligned} \text{Slope} &= \frac{y_2-y_1}{x_2-x_1} \\ \text{Slope} &= \frac{ 2 - 7 }{ 6 - 5 } \\ \text{Slope} &= -5 \end{aligned} \] \[ \begin{aligned} y &= -5 x + b \\ 7 &= -5 \times 5 + b \\ 7 &= -25 + b \\ b &= 32 \end{aligned} \] The slope-intercept form of the line is: \[ y = - 5 x + 32 \]