Plotting Straight-Line Graphs Revision Notes for Edexcel GCSE Maths

Plotting straight-line graphs

Drawing straight-line graphs is a fundamental skill that appears frequently in GCSE mathematics exams. There are two main methods you can use to plot these graphs accurately, and both are equally effective when applied correctly.

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Two Main Methods Available:

Method 1: The table of 3 values method
Method 2: The x = 0, y = 0 method (intercept method)

Both methods will give you the same result, so choose the one that feels more comfortable for you.

Method 1: The table of 3 values method

This method is often considered the easiest approach for plotting straight-line graphs. It works well for any linear equation and provides a reliable way to ensure accuracy.

How the table of 3 values method works

The process involves three straightforward steps:

Choose three values of x - Pick any three numbers that are convenient to work with, ideally within the range you need to graph
Calculate the corresponding y-values - Substitute each x-value into the equation to find the matching y-coordinate
Plot the coordinates and draw the line - Mark all three points on your graph and join them with a straight line

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Worked Example: Using the Table of 3 Values Method

Let's draw the graph of $y = 2x - 3$ for values of x from -1 to 4.

Step 1: Create a table with three suitable x-values: 0, 2, and 4.

Step 2: Substitute each x-value into the equation:

When $x = 0$ : $y = 2(0) - 3 = -3$
When $x = 2$ : $y = 2(2) - 3 = 4 - 3 = 1$
When $x = 4$ : $y = 2(4) - 3 = 8 - 3 = 5$

Step 3: This gives us the coordinates (0, -3), (2, 1), and (4, 5).

When we plot these points and join them, we get a perfectly straight line.

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Checking Your Work: If you're plotting a straight-line equation and your three points don't form a straight line, you know something has gone wrong. This is a brilliant way to check your working - the points must be collinear (in a straight line) if your calculations are correct.

Method 2: The x = 0, y = 0 method

This method is particularly useful when you need to find where a line crosses the axes. It's sometimes called the intercept method because it finds the x-intercept and y-intercept directly.

How the x = 0, y = 0 method works

This method also follows three clear steps:

Set x = 0 in the equation and solve for y - this gives you the y-intercept (where the line crosses the y-axis)
Set y = 0 in the equation and solve for x - this gives you the x-intercept (where the line crosses the x-axis)
Plot these two points and join them with a straight line

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Worked Example: Using the x = 0, y = 0 Method

Let's apply this method to graph $3x + 5y = 15$ between x = -1 and x = 6.

Finding the y-intercept (where x = 0): $3(0) + 5y = 15$ $5y = 15$ $y = 3$

So the line crosses the y-axis at (0, 3).

Finding the x-intercept (where y = 0): $3x + 5(0) = 15$ $3x = 15$ $x = 5$

So the line crosses the x-axis at (5, 0).

Result: Plot the points (0, 3) and (5, 0) and join them with a straight line.

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When to Use the x = 0, y = 0 Method:

This method is particularly effective when:

The equation is given in the form $ax + by = c$
You need to identify the intercepts quickly
You're confident in your algebra skills

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Risk to Consider: There's a small risk involved with this method - if you make an error in calculating one of the intercepts, your entire line will be wrong. Some students prefer the three-point method because it provides an extra check.

Choosing the right method

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Method Selection Guide:

Both methods are valid and will give you the same result. The table of 3 values method offers more security because you can check if your points are collinear. The x = 0, y = 0 method is faster but requires more confidence in your calculations.

Consider your personal preference and the specific equation you're working with when deciding which method to use.

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Key Points to Remember:

Straight-line graphs should always produce points that form a perfectly straight line
If your points don't line up, check your calculations again
Both methods are equally valid - choose the one that feels more comfortable
Practice both methods so you can use either one confidently in your exam
Always use a ruler to draw your final line neatly and accurately

Plotting Straight-Line Graphs (Edexcel GCSE Maths): Revision Notes