Complete the equation of the line through

\[(-9,-9)\] and

\[(-6,0)\].

asked by guest
on Sep 20, 2024 at 1:37 am



You asked:

Find the equation of the line through \((-9, -9)\) and \((-6, 0)\).

MathBot Answer:

Standard Form:

\[ \begin{aligned}Ax + By + C = 0\end{aligned} \] \[ \begin{aligned} \text{Slope} &= -\frac{A}{B} \\ &= \frac{y_2-y_1}{x_2-x_1} \\ -\frac{A}{B} &= \frac{ 0 - -9 }{ -6 - -9 } \\ -\frac{A}{B} &= \frac{ 9 }{ 3 } \\ A =& -9, B = 3 \end{aligned} \] \[ \begin{aligned} -9 x + 3 y + C &= 0 \\ -9(-9) + 3(-9) + C &= 0 \\ + + C &= 0 \\ 81 + C &= 27 \\ C &= 54 \end{aligned} \] An equation of the line in standard form is: \[ - 9 x + 3 y - 54 = 0 \]

Slope-Intercept Form:

\[ y = m x + b \] \[ \begin{aligned} \text{Slope} &= \frac{y_2-y_1}{x_2-x_1} \\ \text{Slope} &= \frac{ 0 - -9 }{ -6 - -9 } \\ \text{Slope} &= 3 \end{aligned} \] \[ \begin{aligned} y &= 3 x + b \\ -9 &= 3 \times -9 + b \\ -9 &= -27 + b \\ b &= 18 \end{aligned} \] The slope-intercept form of the line is: \[ y = 3 x + 18 \]


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