Complete the point-slope equation of the line through

\[(-9,6)\] and

\[(-7,-8)\].

asked by guest
on Sep 20, 2024 at 1:25 am



You asked:

Find the equation of the line through \((-9, 6)\) and \((-7, -8)\).

MathBot Answer:

Standard Form:

\[ \begin{aligned}Ax + By + C = 0\end{aligned} \] \[ \begin{aligned} \text{Slope} &= -\frac{A}{B} \\ &= \frac{y_2-y_1}{x_2-x_1} \\ -\frac{A}{B} &= \frac{ -8 - 6 }{ -7 - -9 } \\ -\frac{A}{B} &= \frac{ -14 }{ 2 } \\ A =& 14, B = 2 \end{aligned} \] \[ \begin{aligned} 14 x + 2 y + C &= 0 \\ 14(-9) + 2(6) + C &= 0 \\ + + C &= 0 \\ 12 + C &= 126 \\ C &= -114 \end{aligned} \] An equation of the line in standard form is: \[ 14 x + 2 y + 114 = 0 \]

Slope-Intercept Form:

\[ y = m x + b \] \[ \begin{aligned} \text{Slope} &= \frac{y_2-y_1}{x_2-x_1} \\ \text{Slope} &= \frac{ -8 - 6 }{ -7 - -9 } \\ \text{Slope} &= -7 \end{aligned} \] \[ \begin{aligned} y &= -7 x + b \\ 6 &= -7 \times -9 + b \\ 6 &= 63 + b \\ b &= -57 \end{aligned} \] The slope-intercept form of the line is: \[ y = - 7 x - 57 \]


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