Linear Equations

Linear Equations - Problem Solving


The graph of (k1)x+y=9k+10(k-1)x+y=9k+10 always passes through the point P=(a,b)P=(a,b) regardless of the value of kk. What is the value of a+ba+b?

What is the square of the length of the line segment that lies in the first quadrant of the Cartesian plane and is part of the line that perpendicularly intersects with the line 4x6y21=04x-6y-21=0 at (3,32)?\left(3,-\frac{3}{2}\right)?

For the linear function f(x)=ax+bf(x)=ax+b, if f(3)=1 and f(x+1)f(x1)=20,f(-3)=-1 \text{ and } f(x+1)-f(x-1)=20, what is the value of f(15)f(15)?

Line segment AB\overline{AB} passes through the origin O=(0,0)O=(0, 0) and the line segments OA\overline{OA} and OB\overline{OB} have equal lengths. Line segment CD\overline{CD} also passes through the origin and the line segments OC \overline{OC} and OD\overline{OD} have equal lengths. If A=(5,22)A=(5, 22) and C=(5,2),C=( -5,2), what is the slope of the line passing through the two points BB and D?D?

What is the sum of all the values of kk that make three points A=(1,k),A=(1,k), B=(k,1)B=(k,1) and C=(10,10)C=(10,10) lie on the same line?


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