Math Problem Solver

Standard Form:

\[ \begin{aligned}Ax + By + C = 0\end{aligned} \] \[ \begin{aligned} \text{Slope} &= -\frac{A}{B} \\ &= \frac{y_2-y_1}{x_2-x_1} \\ -\frac{A}{B} &= \frac{ -3 - 4 }{ 1 - 2 } \\ -\frac{A}{B} &= \frac{ -7 }{ -1 } \\ A =& 7, B = -1 \end{aligned} \] \[ \begin{aligned} 7 x + -1 y + C &= 0 \\ 7(2) + -1(4) + C &= 0 \\ + + C &= 0 \\ 14 + C &= 4 \\ C &= 10 \end{aligned} \] An equation of the line in standard form is: \[ 7 x - y - 10 = 0 \]

Slope-Intercept Form:

\[ y = m x + b \] \[ \begin{aligned} \text{Slope} &= \frac{y_2-y_1}{x_2-x_1} \\ \text{Slope} &= \frac{ -3 - 4 }{ 1 - 2 } \\ \text{Slope} &= 7 \end{aligned} \] \[ \begin{aligned} y &= 7 x + b \\ 4 &= 7 \times 2 + b \\ 4 &= 14 + b \\ b &= -10 \end{aligned} \] The slope-intercept form of the line is: \[ y = 7 x - 10 \]