The graph of line a passes through the points (3,0) and(0,3).The graph of line b has a slope of -2/3 and intercepts the origin.what is the solution to this system of linear equations
step 1
Find the equation of line a
Find the slope
m=(3-0)/(0-3)
m=3/-3
m=-1
the equation of the line in slope intercept form is equal to
y=mx+b
we have
m=-1
b=3
so
y=-x+3 ------> equation line a
step 2
Find the equation line b
m=-2/3
If the line passes through the origin, that means, the equation is of the form
y=mx
we have
m=-2/3
so
y=-(2/3)x -----> equation line b
step 3
Solve the system of equations
y=-x+3 ------> equation line a
y=-(2/3)x -----> equation line b
Equate both equations
-x+3=-(2/3)x
x-(2/3)x=3
(1/3)x=3
x=9
Find the value of y
y=-9+3
y=-6
the solution is (9,-6)