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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 and Lines Warmup


A line passes through the point \((1,3).\) It also passes through exactly 1 of the following points: \[ (0,0), (6,6), (10,10), (3,9), (28,24).\] 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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