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Linear Equations

Your music collection grows by 20 songs every week. If you currently have 1,000 songs, how many weeks will it take to amass 3,500 songs?

Parallel and Perpendicular

         

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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