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Algebra

Linear Equations

Linear Equations - Parallel and Perpendicular Lines

         

What is the \(y\)-intercept of the line that is parallel to the line \( 5x - y - 3 = 0 \) and passes through the point \( (-9, 16) \)?

Two lines \[y=-\frac{1}{4}x+3 \text{ and } y=ax-9\] are perpendicular to each other. What is the value of \(a ?\)

The \(2\) lines

\[mx-4y-5m+3=0, \\ 12x+(m+17)y+7m-29=0\]

are perpendicular to each other for some real number \(m\). What is \(m\)?

If the two sets in the Cartesian plane \[\] \[\begin{align} A &= \{(x,y) \mid x+ay+1=0\} \\ B &= \{(x,y) \mid 3x-by+1=0\} \end{align}\] \[\] satisfy \(A \cap B=\emptyset,\) what is the value of \(\frac{b}{a}?\)

Line \(AB\) passes through two points \( A=(7,\ 10)\) and \(B=(10,\ 9) \). If a line is perpendicular to line \(AB\) and passes through points \( (-5,\ 12) \) and \( (2,\ a) \), what is the value of \( a \)?

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