Math Problem Solver

Standard Form:

\[ \begin{aligned}Ax + By + C = 0\end{aligned} \] \[ \begin{aligned} \text{Slope} &= -\frac{A}{B} \\ &= \frac{y_2-y_1}{x_2-x_1} \\ -\frac{A}{B} &= \frac{ -3 - 8.25 }{ 1.86 - -1.5 } \\ -\frac{A}{B} &= \frac{ - \frac{45}{4} }{ \frac{84}{25} } \\ A =& \frac{45}{4}, B = \frac{84}{25} \end{aligned} \] \[ \begin{aligned} \frac{45}{4} x + \frac{84}{25} y + C &= 0 \\ \frac{45}{4}(-1.5) + \frac{84}{25}(8.25) + C &= 0 \\ + + C &= 0 \\ \frac{672}{25} + 84 \cdot \frac{1}{100} + C &= \frac{45 \cdot \left(1 + 5 \cdot \frac{1}{10}\right)}{4} \\ C &= \frac{672}{25} + \frac{21}{25} - \frac{45 \cdot \left(1 + 5 \cdot \frac{1}{10}\right)}{4} \end{aligned} \] An equation of the line in standard form is: \[ 2250 x + 672 y - 2169 = 0 \]

Slope-Intercept Form:

\[ y = m x + b \] \[ \begin{aligned} \text{Slope} &= \frac{y_2-y_1}{x_2-x_1} \\ \text{Slope} &= \frac{ -3 - 8.25 }{ 1.86 - -1.5 } \\ \text{Slope} &= - \frac{375}{112} \end{aligned} \] \[ \begin{aligned} y &= - \frac{375}{112} x + b \\ 8.25 &= - \frac{375}{112} \times -1.5 + b \\ 8.25 &= \frac{375 \cdot \left(1 + 5 \cdot \frac{1}{10}\right)}{112} + b \\ b &= \frac{723}{224} \end{aligned} \] The slope-intercept form of the line is: \[ y = - \frac{375 x}{112} + \frac{723}{224} \]