Algebra

Linear Equations

Linear Equations - Parallel and Perpendicular Lines

         

What is the yy-intercept of the line that is parallel to the line 5xy3=0 5x - y - 3 = 0 and passes through the point (9,16) (-9, 16) ?

Two lines y=14x+3 and y=ax9y=-\frac{1}{4}x+3 \text{ and } y=ax-9 are perpendicular to each other. What is the value of a?a ?

The 22 lines

mx4y5m+3=0,12x+(m+17)y+7m29=0mx-4y-5m+3=0, \\ 12x+(m+17)y+7m-29=0

are perpendicular to each other for some real number mm. What is mm?

If the two sets in the Cartesian plane A={(x,y)x+ay+1=0}B={(x,y)3xby+1=0}\begin{aligned} A &= \{(x,y) \mid x+ay+1=0\} \\ B &= \{(x,y) \mid 3x-by+1=0\} \end{aligned} satisfy AB=,A \cap B=\emptyset, what is the value of ba?\frac{b}{a}?

Line ABAB passes through two points A=(7, 10) A=(7,\ 10) and B=(10, 9)B=(10,\ 9) . If a line is perpendicular to line ABAB and passes through points (5, 12) (-5,\ 12) and (2, a) (2,\ a) , what is the value of a a ?

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