Math Problem Solver

Standard Form:

\[ \begin{aligned}Ax + By + C = 0\end{aligned} \] \[ \begin{aligned} \text{Slope} &= -\frac{A}{B} \\ &= \frac{y_2-y_1}{x_2-x_1} \\ -\frac{A}{B} &= \frac{ -4 - -5 }{ -4 - -6 } \\ -\frac{A}{B} &= \frac{ 1 }{ 2 } \\ A =& -1, B = 2 \end{aligned} \] \[ \begin{aligned} -1 x + 2 y + C &= 0 \\ -1(-6) + 2(-5) + C &= 0 \\ + + C &= 0 \\ 6 + C &= 10 \\ C &= -4 \end{aligned} \] An equation of the line in standard form is: \[ - x + 2 y + 4 = 0 \]

Slope-Intercept Form:

\[ y = m x + b \] \[ \begin{aligned} \text{Slope} &= \frac{y_2-y_1}{x_2-x_1} \\ \text{Slope} &= \frac{ -4 - -5 }{ -4 - -6 } \\ \text{Slope} &= \frac{1}{2} \end{aligned} \] \[ \begin{aligned} y &= \frac{1}{2} x + b \\ -5 &= \frac{1}{2} \times -6 + b \\ -5 &= -3 + b \\ b &= -2 \end{aligned} \] The slope-intercept form of the line is: \[ y = \frac{x}{2} - 2 \]