Year 9 Maths Straight-Line Graphs Made Simple
Straight-line graphs connect equations to shapes. In Year 9, pupils should plot coordinates, understand gradient, identify a y-intercept and interpret equations such as y = 2x + 3. The central idea is that one variable changes at a constant rate in relation to another. The equation, table of values and line on the axes are different ways of describing that same relationship.
Plot points using x then y
A coordinate (2, 5) means move two units to the right and five units up from the origin. Negative x lies left and negative y lies below. Check the units marked on each axis before plotting. One square might represent one, two or five units. Plot several points carefully and use a ruler when joining points that are supposed to lie on a straight line.
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Make a table for y = 2x + 3
Choose x-values −1, 0, 1 and 2. Substituting gives y-values 1, 3, 5 and 7. Plot (−1,1), (0,3), (1,5) and (2,7). They lie on one straight line because y changes by two whenever x increases by one. Any point can be checked by substituting its coordinates into the equation. This is a reliable method when an equation looks unfamiliar.
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Understand gradient as change
The gradient of y = 2x + 3 is 2: moving one unit right increases y by two. In y = −3x + 1, y decreases by three for every one-unit increase in x. A negative gradient means a falling line as you move to the right. Gradient can also represent a price per item, speed or another rate of change, depending on what the axes measure.
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Read the y-intercept
In y = mx + c, the y-intercept is c, the value of y when x = 0. For y = 2x + 3, the y-intercept is (0,3). The x-intercept is different: put y = 0 and solve 0 = 2x + 3, giving x = −1.5. Naming the correct axis helps prevent confusion between these two features.
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Calculate gradient from two points
For points (1,4) and (4,10), the change in y is 10 − 4 = 6 and the change in x is 4 − 1 = 3. Gradient = 6/3 = 2. Keep subtraction order consistent. To find the equation, substitute (1,4) into y = 2x + c, giving c = 2, so the line is y = 2x + 2. Check using the second point: 10 = 2(4) + 2.
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Interpret a real situation
A taxi charging £4 at the start plus £2 per kilometre can be represented by C = 2d + 4. The gradient represents the extra cost per kilometre and the intercept the initial charge. Negative distances make no sense in this context, so the meaningful part of the graph starts at d = 0. Modelling links straight-line graphs to everyday reasoning and GCSE functions.
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Frequently asked questions
Must a gradient be a whole number?
No, it can be fractional, negative or zero.
How do I check a plotted point?
Substitute its x-coordinate into the equation and compare the result with its y-coordinate.
Explore further KS3 resources
The related resources below address supporting skills. Choose those that match the specific questions you find difficult rather than reading every article in one sitting.
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