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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?

Linear Equations Warmup

         

A line passes through the point \((1,3).\) It also passes through exactly 1 of the following points: \[\begin{array} &(0,0), &(6,6), &(10,10), &(3,9), &(28,24).\end{array}\] What is the slope of the line?

What is the equation of a line that passes through the points \((3,4)\) and \((a,b)\), assuming \(a\neq3\) and \(b\neq4\)?

The line \(L\) passes through the point \((4,4)\), has slope \(m\) such that \(m<-1\), and has \(x\)-intercept \(a\) and \(y\)-intercept \(b\) such that \(a+b=18\).

What is the value of \(b\)?

There is one point \((a,b)\) such that the line \((k-3)x + (2k+1)y = 14\) passes through \((a,b)\) for all real values of \(k\).

Find \(a+b\).

Two distinct points \((a,b)\) and \((b,c)\) lie on the line \(y=-x+5\) What is the value of \(a-c\)?

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