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.

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

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

Check the answer: 2(-1.5) + 3 = 0✔

Answer: `x = -1.5`

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✔

Answer: `x = 3.5`

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

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