Question

Russ is solving an equation where both sides are linear expressions. He graphs the expressions and finds that they are the same line. How should Russ interpret this outcome? There is no intersection point. There is exactly one intersection point. There are exactly two intersection points. There are infinitely many intersection points.

Answer 1

If the lines are the same, then ...
  "There are infinitely many intersection points." . . . . . 4th selection

Answer 2

Answer is ''there are infinitely many intersection points'' .

Let equation of the line 1  be    

$a_{1}x+b_{1}y=c_{1}\\\text{and equation of line 2 be}\\a_{2}x+b_{2}y=c_{2}$

As given they are the same line so Russ should interpret that

$\frac{a_{1}}{a_{2}}= \frac{b_{1}}{b_{2}}=\frac{c_{1}}{c_{2}}$

So, they are coincident and its a consistent-dependent system .Both of them will have same values of y for same value of x .

Therefore they will have infinitely many solutions and hence intersections.

For example Equation of line 1 be 2x +3y = 5 and equation of line 2 be 4x+6y=10 then  

$\frac{2}{4}=\frac{3}{6}=\frac{5}{10}=\frac{1}{2}$  

therefore, these lines are coincident and have infinitely many solutions .