Graphing Axes

Question

Graph each pair of lines on the same set of axes. Determine the point of intersection of the two lines. Note that you may have to estimate the coordinates.

 

1) y=2x-4 and y=4x+2

 

 

2)2x-5 and y=-x+7

Answer 1

Two points determine a line.  Just "connect the dots" and keep on going in each direction.

 

Quite often, the intercepts (y-intercept when x=0 and x-intercept when y=0) are easy to determine.  Otherwise, use a convenient integer to avoid fractions (unless you really like fractions).

 

1) y=2x-4

     has points:  (0,-4) and (2,0)  and (-3,-10)

   and y=4x+2

     has points:  (0,2) and (-3,-10)

   So, the point (-3,-10) should be where they intersect (solves both equations). 
 
2) y=2x-5

    has points:  (0,-5) and (1,-3)  and (4,3)

   and y=-x+7 has points:   (0,7) and (1,6) and (4,3)

  So, the point (4,3) is where they intersect.