Linear Graphs
Plot coordinates, draw straight-line graphs from equations like y = 2x + 1, and identify gradient and intercept.
Overview
A linear graph is a straight line drawn from an equation such as y = 2x + 1. In Year 8 students plot coordinates in all four quadrants, build a table of values from an equation, and draw the matching straight line. They also start to read the gradient (steepness) and the y-intercept (where the line crosses the y-axis) — the foundations of the whole topic of graphs.
What You Will Learn
- Plot and read coordinates in all four quadrants
- Complete a table of values for a linear equation
- Draw the straight-line graph of an equation such as y = 2x + 1
- Identify the gradient and y-intercept of a line in the form y = mx + c
- Recognise horizontal and vertical lines such as y = 3 and x = −2
Key Vocabulary
Common Mistakes to Avoid
- Plotting coordinates the wrong way round (it is across then up: (x, y))
- Making an arithmetic slip in the table of values, so one point is off the line
- Confusing the gradient with the y-intercept in y = mx + c
- Joining the points with a wobbly or curved line instead of a ruler-straight one
What Comes Next
In Year 9 and at IGCSE this grows into finding the equation of a line, the gradient formula, and graphs of quadratics and other curves, within the IGCSE Algebra and Graphs and Coordinate Geometry topics.
Frequently Asked Questions
What do the m and c mean in y = mx + c?
m is the gradient — how steep the line is and whether it slopes up or down. c is the y-intercept — the value of y where the line crosses the y-axis. In y = 2x + 1, the gradient is 2 and the line crosses the y-axis at 1.
How do I draw a straight-line graph from an equation?
Choose a few values of x, substitute each into the equation to find y, and write the pairs as coordinates. Plot the points and join them with a straight line using a ruler.
Study This Topic
Topic Details
- Stage
- Year 8
- Strand
- Algebra
- Framework ref
- 8As
- Difficulty
- Medium
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) →