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Using Graphs to Solve Equations

Using Graphs to Solve Equations

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.

In order to plot the graph correctly, you may have to re-arrange the equation as one side of the equation must equal zero.

Example 1

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

Graph of y = 2x + 3

The line crosses the `x`-axis at - 1.5

Check the answer: 2(-1.5) + 3 = 0✔

Answer: `x = -1.5`

Example 2

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

It is necessary for one side of the equation to equal zero

Subtract 3 from both sides of the equation to get `-2x + 7 = 0`

Plot the graph using three points

The line crosses the `x`-axis at `x` = 3.5

Check the answer: -2(2.5) + 10 = 3✔

Graph of y = -2x + 7

Answer: `x = 3.5`

See also y=mx+c and Equation of a Line