How Do You Check a Solution with the Intersection of Graphs Method?

The solution to an equation may be checked by graphing each side of the equation with a graphing utility. The solution to the equation should correspond to the input value at the point of intersection.

In each of the problems below, students have solved an equation algebraically and then checked the solution on a graph.

Problem 1 Solve

\displaystyle 5x-14=23+7x

m152_int_graph_meth_5

Problem 2 Solve

\displaystyle 5.92t=1.78t-4.14

m152_int_graph_meth_1

Problem 3 Solve

\displaystyle x-\frac{5}{6}=3x+\frac{1}{4}

m152_int_graph_meth_3

Problem 4 Solve

\displaystyle 5\left( y-6 \right)=18-2y

m152_int_graph_meth_4

 

Note that in each case the students have included an exact answer such as a fraction as well as an approximate answer. The approximate answer is appropriate for comparing to the point of intersection which is also an approximate solution.