Using Graphs to Solve Equations

Using Graphs to Solve Equations

GCSE(F), GCSE(H),

Graphs can be used to estimate solutions to equations.

The solution to the equation is given where the graph crosses the x-axis. For some types of graphs, such as quadratics, there may be more than one solution if the line crosses the x-axis more than once. There may also be no solutions if the the line does not cross the x-axis at all.

When a solution is found, substitute back into the equation to check the answer.

Examples

1. The graph shows the function 2x + 3. What is the solution to 2x + 3 = 0?

graph of 2x+3

Answer: x = -1.5

The line crosses the x-axis at - 1.5. Check the answer: 2(-1.5) + 3 = 0, which is true.

2. By drawing a graph, obtain the solution for -2x + 10 = 3.

Answer: x = 3.5

Rearrange the equation to -2x + 7 = 0 and plot the graph. The line crosses the x-axis at x = 3.5. Check the answer: -2(2.5) + 10 = 3, which is true.

graph of -2x + 7