Math Problem Solver

Standard Form:

\[ \begin{aligned}Ax + By + C = 0\end{aligned} \] \[ \begin{aligned} \text{Slope} &= -\frac{A}{B} \\ &= \frac{y_2-y_1}{x_2-x_1} \\ -\frac{A}{B} &= \frac{ 7 - 8 }{ 4 - 3 } \\ -\frac{A}{B} &= \frac{ -1 }{ 1 } \\ A =& 1, B = 1 \end{aligned} \] \[ \begin{aligned} 1 x + 1 y + C &= 0 \\ 1(3) + 1(8) + C &= 0 \\ + + C &= 0 \\ 8 + C &= -3 \\ C &= 11 \end{aligned} \] An equation of the line in standard form is: \[ x + y - 11 = 0 \]

Slope-Intercept Form:

\[ y = m x + b \] \[ \begin{aligned} \text{Slope} &= \frac{y_2-y_1}{x_2-x_1} \\ \text{Slope} &= \frac{ 7 - 8 }{ 4 - 3 } \\ \text{Slope} &= -1 \end{aligned} \] \[ \begin{aligned} y &= -1 x + b \\ 8 &= -1 \times 3 + b \\ 8 &= -3 + b \\ b &= 11 \end{aligned} \] The slope-intercept form of the line is: \[ y = - x + 11 \]