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Linear Equations

Linear Equations and Lines Warmup


A line passes through the point (1,3).(1,3). It also passes through exactly 1 of the following points: (0,0),(6,6),(10,10),(3,9),(28,24). (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)(3,4) and (a,b)(a,b), assuming a3a\neq3 and b4b\neq4?

The line LL passes through the point (4,4)(4,4), has slope mm such that m<1m<-1, and has xx-intercept aa and yy-intercept bb such that a+b=18a+b=18.

What is the value of bb?

There is one point (a,b)(a,b) such that the line (k3)x+(2k+1)y=14(k-3)x + (2k+1)y = 14 passes through (a,b)(a,b) for all real values of kk.

Find a+ba+b.

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


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