y=1/3x+1 to y=-3x+11

Question

How do u do this problem? Please help me for my grade

Answer 1

Each of the equations are already in "slope-intercept" form (y=mx+b)

making the information needed for graphing readily available.

 

y=(1/3)x+1.......Eq1, given, problem statement

     m=1/3.........slope Eq1, vertical "rise" of 1, horizontal "run" of 3.

     y-intercept is (0,1)...point where Eq1 line crosses the y-axis.

 

Plot point (0,1) on your graph.  From that point using the slope value, go up 1 unit (positive), go 3 units left (also positive).  You should now be at point (3,2).  Draw a line with a ruler through points (0,1) and (3,2).

 

 

y=-3x+11..........Eq2, given, problem statement

      m=-3/1.......slope Eq2, vertical "rise" of -3, horizontal "run" of 1.

      y-intercept is (0,11)...point where Eq2 line crosses the y-axis.

 

Plot point (0,11) on your graph.  From that point using the slope value, go down 3 units (negative), go 1 unit right (positive).  You should now be at point (1,8).  Draw a line with a ruler through points (0,11) and (1,8).

 

 

Now look at your graph and find the coordinates where the two lines intersect.  That point has coordinates (3,2).  If we substitute that point (x=3,y=2) into Eq1 and Eq2, we should get true statements.  Let's check...

 

2=(1/3)3+1.....Eq1, substitute values for "x and y".

2=1+1............simplify

2=2................true, √check

 

2=(-3)3+11.....Eq2, substitute values for "x and y".

2=-9+11.........simplify

2=2................true, √check

 

Always check your solutions and work!!

 

Now try solving the same two equations by "substitution" and "elimination" methods.  You should get the same values for "x and y".