Math Problem Solver

Standard Form:

\[ \begin{aligned}Ax + By + C = 0\end{aligned} \] \[ \begin{aligned} \text{Slope} &= -\frac{A}{B} \\ &= \frac{y_2-y_1}{x_2-x_1} \\ -\frac{A}{B} &= \frac{ 11 - 10 }{ 8 - 6 } \\ -\frac{A}{B} &= \frac{ 1 }{ 2 } \\ A =& -1, B = 2 \end{aligned} \] \[ \begin{aligned} -1 x + 2 y + C &= 0 \\ -1(6) + 2(10) + C &= 0 \\ + + C &= 0 \\ 20 + C &= 6 \\ C &= 14 \end{aligned} \] An equation of the line in standard form is: \[ - x + 2 y - 14 = 0 \]

Slope-Intercept Form:

\[ y = m x + b \] \[ \begin{aligned} \text{Slope} &= \frac{y_2-y_1}{x_2-x_1} \\ \text{Slope} &= \frac{ 11 - 10 }{ 8 - 6 } \\ \text{Slope} &= \frac{1}{2} \end{aligned} \] \[ \begin{aligned} y &= \frac{1}{2} x + b \\ 10 &= \frac{1}{2} \times 6 + b \\ 10 &= 3 + b \\ b &= 7 \end{aligned} \] The slope-intercept form of the line is: \[ y = \frac{x}{2} + 7 \]