Solving Equations with graphs

An equation allows you to express the relationship between different quantities. It is typically shaped like “x = y”.
An equation becomes a linear equation when the highest power of the variable is one. They form straight lines when plotted on a graph.
Non-linear equations are equations where the variable has a power greater than one or less than one. The graph of a non-linear equation is typically a curve.

Points on a graph are typically labelled with an x-value (horizontal or ‘along’) and a y-value (vertical or ‘up’).
When drawing a graph, start by plotting a few key points and then join them up.
The point where the graph meets the x-axis is known as the x-intercept. When the graph intersects the y-axis, it’s called the y-intercept.

The solution to an equation is the value or set of values which makes the equation true.
If solving a linear equation, the solution will be the point where the line crosses the x-axis.
In non-linear equations, there can be more than one solution. The graph will cross the x-axis at each solution.
When two lines intersect on a graph, the coordinates of the point of intersection provide the solution to the system of equations represented by the two lines.

Linear graphs are straight lines which usually have the equation ‘y = mx + c’. Here, ‘m’ is the gradient and ‘c’ is the y-intercept.
A graph that forms a curved line, typically represented by the equation ‘y = x^2’, is a quadratic graph.
Cubic graphs will have one variable to the power of three and generally take shape as a curve with a single or double bend.

Being able to read and interpret a graph is essential. The scale, labels, and units provide key information about what a graph is representing.
The gradient of a line reflects how steep it is, and can be found by dividing the vertical change by the horizontal change.
As well as finding solutions, graphs can also be useful for comparing data, spotting patterns, and predicting outcomes.

Study, practise, and be sure to understand these concepts to improve your problem-solving skills in Mathematics.