Drawing Straight Line Graphs Revision Notes for AQA GCSE Maths

Drawing straight line graphs

When you need to sketch or draw a straight line graph, there are three main methods you can use. Each has its own advantages depending on the situation and how the equation is presented to you.

Method 1: The table of 3 values method

This is often the most reliable method, especially when you want to be absolutely certain your graph is accurate. Here's how it works:

Step 1: Create a table Choose three suitable x-values that will be easy to work with. It's often good to pick values that are evenly spaced, such as consecutive integers or values around zero.

Step 2: Calculate the y-values Substitute each x-value into the equation to find the corresponding y-value. Make sure to follow the correct order of operations when doing your calculations.

Step 3: Plot the points and draw the line Once you have your three coordinate pairs, plot them on your graph. If your equation is correct and your calculations are accurate, these three points should form a perfectly straight line. If they don't align, you'll need to check your working.

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Worked Example: Using the table of 3 values method

If you're drawing $y = -2x + 4$ , you might choose x-values of 0, 2, and 4.

Step 1: Create your table with chosen x-values Step 2: Calculate y-values by substitution:

When $x = 0$ : $y = -2(0) + 4 = 4$
When $x = 2$ : $y = -2(2) + 4 = 0$
When $x = 4$ : $y = -2(4) + 4 = -4$

Step 3: Plot the coordinates $(0, 4)$ , $(2, 0)$ , and $(4, -4)$ , then draw your straight line through them.

Method 2: Using y = mx + c

This method is particularly useful when your equation is already in the standard form $y = mx + c$ , or when you can easily rearrange it into this form.

Step 1: Rearrange the equation If necessary, rearrange your equation so that y is the subject and it's in the form $y = mx + c$ , where m is the gradient and c is the y-intercept.

Step 2: Plot the y-intercept The value of c tells you where the line crosses the y-axis. Put a dot at the point $(0, c)$ on your graph.

Step 3: Use the gradient to find more points The gradient m tells you how the line moves. For every 1 unit you move to the right (positive x-direction), the line moves m units up (if m is positive) or down (if m is negative). From your y-intercept point, use this pattern to mark several more points.

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Remember that gradient represents the "rise over run" - it shows how steep the line is and which direction it slopes.

Step 4: Draw the line Once you have plotted 4 or 5 points using the gradient, draw a straight line through them.

Step 5: Check your gradient Look at your finished line and verify that the gradient appears correct. A positive gradient should slope upward from left to right, whilst a negative gradient should slope downward.

Method 3: The x = 0, y = 0 method

This method is excellent for quick sketches and works by finding where the line crosses both axes.

Step 1: Find the y-intercept Set $x = 0$ in your equation and solve for y. This gives you the point where the line crosses the y-axis.

Step 2: Find the x-intercept Set $y = 0$ in your equation and solve for x. This gives you the point where the line crosses the x-axis.

Step 3: Plot and draw Mark these two intercept points on your graph and draw a straight line passing through both of them.

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Worked Example: Using the intercept method

With the equation $y = 3x - 5$ :

Step 1: Find y-intercept by setting $x = 0$ $y = 3(0) - 5 = -5$ So the line crosses the y-axis at $(0, -5)$

Step 2: Find x-intercept by setting $y = 0$ $0 = 3x - 5$ $3x = 5$ $x = \frac{5}{3}$ So the line crosses the x-axis at $\left(\frac{5}{3}, 0\right)$

Step 3: Plot both intercept points and draw a straight line through them.

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Choosing the right method

The table of 3 values method is most reliable when you need precision and want to double-check your work. The $y = mx + c$ method is efficient when the equation is already in standard form or easily rearranged. The intercept method is perfect for quick sketches and when you need to identify key features of the line quickly.

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Remember that whichever method you choose, your final graph should show a perfectly straight line. If your points don't align properly, it's worth checking your calculations before proceeding.

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Key Points to Remember:

All three methods should give you the same straight line for any given equation
The table of 3 values method is most reliable for checking your work
The $y = mx + c$ method is efficient when you can easily identify the gradient and y-intercept
The intercept method is quickest for sketching graphs
Always check that your plotted points form a straight line - if they don't, review your calculations

Drawing Straight Line Graphs (AQA GCSE Maths): Revision Notes