Lesson 24 · Equations, Inequalities and Line Graphs

Graphs of Equations in Two Variables

MathematicsSubject
14 minEstimated read
A graph is an equation you can look at

Every point on the line is a pair that works, and every pair that works is on the line.

Coordinates, briefly

The x value first, the y value second. The point (3, 2) is three along and two up, and the order matters.

Three points, not two

Two points fix a line, but always plot a third. If one is out of line you know at once there is an error, and which value to recheck.

Drawing the graph of an equation

Step What to do
1Choose three easy values of x, such as 0, 1 and 2
2Work out y for each and put them in a small table
3Plot the three points, along first and then up
4Check they are in a row, then join them with a ruled line
A line, not a set of dots

Every point between them works too, including ones with fractions in. Three separate dots claim that only three pairs satisfy the equation.

Reading the equation from the line

In y = mx + c, the c is where the line crosses the vertical axis, and the m is how far it rises for every step to the right.

Every point on the line is a solution

Read off the coordinates of any point on the line and put them into the equation. Both sides come out equal, every single time.

Number the axes evenly, and label them

Unequal squares bend a straight line into something that is not straight. The numbers may all be correct while the picture tells a lie.

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