Linear Equations and Lines Warmup Practice Problems Online

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 \(b\neq4\)?

\[(a-3)x+(b-4)y+4b+3a = 0\] \[(a-3)x+(b-4)y+4a-3b = 0\] \[(b-4)x+(3-a)y+4a-3b = 0\] \[(b-4)x+(3-a)y+4b-3a = 0\] \[(b-3)x+(a-4)y+4a-3b = 0\] \[(b-4)x+(a-3)y+4b+3a = 0\]

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 \(b\)?

6 14 \[\frac{20}{3}\] 12 9 10 8

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 \(a-c\)?

\[2b\] 2 -2 0 \[b^2\] \[b\] \[-2b\]

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Linear Equations and Lines Warmup

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Linear Equations