Math Problem Solver

Standard Form:

\[ \begin{aligned}Ax + By + C = 0\end{aligned} \] \[ \begin{aligned} \text{Slope} &= -\frac{A}{B} \\ &= \frac{y_2-y_1}{x_2-x_1} \\ -\frac{A}{B} &= \frac{ 7 - 25 }{ 4 - 10 } \\ -\frac{A}{B} &= \frac{ -18 }{ -6 } \\ A =& 18, B = -6 \end{aligned} \] \[ \begin{aligned} 18 x + -6 y + C &= 0 \\ 18(10) + -6(25) + C &= 0 \\ + + C &= 0 \\ 180 + C &= 150 \\ C &= 30 \end{aligned} \] An equation of the line in standard form is: \[ 18 x - 6 y - 30 = 0 \]

Slope-Intercept Form:

\[ y = m x + b \] \[ \begin{aligned} \text{Slope} &= \frac{y_2-y_1}{x_2-x_1} \\ \text{Slope} &= \frac{ 7 - 25 }{ 4 - 10 } \\ \text{Slope} &= 3 \end{aligned} \] \[ \begin{aligned} y &= 3 x + b \\ 25 &= 3 \times 10 + b \\ 25 &= 30 + b \\ b &= -5 \end{aligned} \] The slope-intercept form of the line is: \[ y = 3 x - 5 \]