Math Problem Solver

Standard Form:

\[ \begin{aligned}Ax + By + C = 0\end{aligned} \] \[ \begin{aligned} \text{Slope} &= -\frac{A}{B} \\ &= \frac{y_2-y_1}{x_2-x_1} \\ -\frac{A}{B} &= \frac{ 5 - 1 }{ -4 - -2 } \\ -\frac{A}{B} &= \frac{ 4 }{ -2 } \\ A =& -4, B = -2 \end{aligned} \] \[ \begin{aligned} -4 x + -2 y + C &= 0 \\ -4(-2) + -2(1) + C &= 0 \\ + + C &= 0 \\ 8 + C &= 2 \\ C &= 6 \end{aligned} \] An equation of the line in standard form is: \[ - 4 x - 2 y - 6 = 0 \]

Slope-Intercept Form:

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