Linear Graphs — Year 8 Revision Notes
These notes cover plotting coordinates, drawing the graph of a linear equation, and reading the gradient and y-intercept — all at Year 8 (Stage 8) level.
Coordinates and quadrants
Coordinates are written as (x, y): the first number is across (the x-axis) and the second is up or down (the y-axis). The axes divide the grid into four quadrants, and coordinates can be positive or negative. The point (−3, 2) is 3 left and 2 up.
Key Facts & Formulas
- Coordinates are (x, y)
- (across, up)
Tips
- Always go across before up.
- Watch the signs in the negative quadrants.
Drawing a linear graph
To draw the graph of y = 2x + 1, make a table of values: choose some x values, work out each y, and plot the points. For x = 0, 1, 2 you get y = 1, 3, 5. Join the points with a straight line using a ruler and extend it across the grid.
Key Facts & Formulas
- y = 2x + 1
- x = 0 → y = 1; x = 1 → y = 3
Tips
- Use at least three points so you can spot a mistake.
- Always join the points with a ruler.
Gradient and intercept
In the form y = mx + c, m is the gradient (steepness) and c is the y-intercept (where the line crosses the y-axis). A positive gradient slopes up to the right and a negative gradient slopes down. Horizontal lines have the form y = a number, and vertical lines have the form x = a number.
Key Facts & Formulas
- y = mx + c
- m = gradient, c = y-intercept
- y = 3 is horizontal; x = −2 is vertical
Tips
- The number with x is the gradient; the number on its own is the intercept.
- y = constant is horizontal; x = constant is vertical.
Revision Checklist
- I can plot and read coordinates in all four quadrants
- I can complete a table of values for a linear equation
- I can draw the straight-line graph of an equation
- I can identify the gradient and y-intercept of a line
Frequently Asked Questions
How can I tell if a line slopes up or down?
Look at the gradient (the number with x). A positive gradient, like in y = 2x + 1, slopes upwards from left to right. A negative gradient, like in y = −2x + 1, slopes downwards.
Build strong foundations in Linear Graphs
A free trial class with Teacher Rig helps your Year 8 child master Linear Graphs now — so IGCSE Maths feels familiar, not frightening, later.
Heading toward IGCSE? See how Linear Graphs develops in IGCSE Algebra and Graphs (Cambridge 0580) →