Math Problem Solver

Standard Form:

\[ \begin{aligned}Ax + By + C = 0\end{aligned} \] \[ \begin{aligned} \text{Slope} &= -\frac{A}{B} \\ &= \frac{y_2-y_1}{x_2-x_1} \\ -\frac{A}{B} &= \frac{ 36 - 571 }{ 6 - 5.1 } \\ -\frac{A}{B} &= \frac{ -535 }{ \frac{9}{10} } \\ A =& 535, B = \frac{9}{10} \end{aligned} \] \[ \begin{aligned} 535 x + \frac{9}{10} y + C &= 0 \\ 535(5.1) + \frac{9}{10}(571) + C &= 0 \\ + + C &= 0 \\ 2675 + 535 \cdot \frac{1}{10} + C &= - \frac{5139}{10} \\ C &= \frac{31889}{10} + \frac{107}{2} \end{aligned} \] An equation of the line in standard form is: \[ 5350 x + 9 y - 32424 = 0 \]

Slope-Intercept Form:

\[ y = m x + b \] \[ \begin{aligned} \text{Slope} &= \frac{y_2-y_1}{x_2-x_1} \\ \text{Slope} &= \frac{ 36 - 571 }{ 6 - 5.1 } \\ \text{Slope} &= - \frac{5350}{9} \end{aligned} \] \[ \begin{aligned} y &= - \frac{5350}{9} x + b \\ 571 &= - \frac{5350}{9} \times 5.1 + b \\ 571 &= - \frac{26750}{9} - \frac{535}{9} + b \\ b &= \frac{10808}{3} \end{aligned} \] The slope-intercept form of the line is: \[ y = - \frac{5350 x}{9} + \frac{10808}{3} \]