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Algebra

# 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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