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📐 Mathematics - Class 7
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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Worked Example 1

Draw the graph of y = 2x + 1.

Choose easy values of xx = 0, 1 and 2
Work out y for each(0, 1), (1, 3) and (2, 5)
Plot and checkAll three in a row, or recheck before drawing
Join with a ruler and extendExtend the line past the points in both directions
Worked Example 2

Is (4, 9) on the line y = 2x + 1? What about (4, 8)?

Substitute the x value2(4) + 1 = 9
Compare with the y value(4, 9) is on the line
Now test the other(4, 8) is not on the line, sitting one unit below it
Why this test mattersIt works without drawing anything, and it checks a graph you have already drawn.
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Activity 24.3

The human graph

What you needTwo chalked axes on the floor meeting at a corner, marked evenly from 0 to 6.
MethodEach student works out their own y for the called equation and stands at their point.
Then change itCall out y = 2x + 4, then y = 3x + 1, and watch what changes.
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1

An equation with two letters has a whole family of solutions, not one.

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1What does the graph of an equation actually show?
2Why should you plot three points when two are enough to draw a line?
3What do m and c tell you in the equation y = mx + c?
4How do you tell whether a given point lies on a line, without drawing it?
5Why must the points be joined into a line, and why must the axes be evenly numbered?

Question 1 of 10

1The point (3, 2) means
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Slide 1 of 4
Unit 24 · Graphs

Graphs of Linear Equations

Mathematics · Grade 7

What You Will Be Able To Do

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Plot points accurately, with the x value always read first

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Draw the graph of an equation from a small table of values

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Read the gradient and the crossing point straight off the equation

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Test whether any point lies on a line, without drawing anything

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Every point on the line is a pair that makes the equation true, and every pair that makes it true is on the line. That is the whole idea of a graph.

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Presenter notes: Open by writing y equals 2x plus 1 on the board and asking for the answer. Somebody will point out that there is not one, which is exactly right and is the whole starting point. Then ask for any pair of numbers that fits, collect five or six from around the room, and say that today they will find out what shape all those answers make when you put them on paper.