Geometry

Equation of a Line

Linear Equations - Intersection of Lines

         

In the graph above, l1 l_1 is a horizontal line with y y-intercept 3 3, and l2 l_2 has a slope of 22 with yy-intercept 1-1. Find the coordinates of the intersection point of the two lines.

What is the interval of all possible values of aa such that the two lines x+y=ax+y=\lvert a \rvert and axy=196ax-y=196 intersect in the first quadrant?

Consider the line passing through two points (5,0)(5, 0) and (0,5)(0, -5). Consider another line passing through two points (4,0)(-4, 0) and (0,2)(0, -2). If these two lines and a third line y=ax85y=ax-85 intersect at one point, what is the value of the constant aa?

A line passing through the intersection point of the two lines x+2y+3=0    and    2xy+a2=0 x+2y+3=0\;\;\text{and}\;\; 2x-y+\frac{a}{2}=0 also passes through two other points (9, 8)  (9,\ -8)\ and  (17, 9)\ (-17,\ 9) . What is the value of a a ?

Suppose the intersection point of the two lines x2y9=0,2x+3y53=0x-2y-9=0, 2x+3y-53=0

is P=(a,b)P=(a,b). What is the value of a+ba+b?

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