Last reviewed: 7 November 2026
Updated November 2026. These Grade 8 coordinates and graphs notes show how to draw and label a Cartesian plane, plot points, make a table of values for a linear equation, choose a suitable scale, draw a straight-line graph, and solve two simultaneous linear equations by graph. The solution of two simultaneous equations is the point where their lines cross. For example, the lines y = x + 1 and x + y = 5 cross at (2, 3), so x = 2 and y = 3.
The examples and questions are original practice for Kenyan junior school learners, not an official paper. For the other Grade 8 maths topics, see our Grade 8 mathematics revision guide and the Grade 8 notes hub.
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What the Grade 8 Curriculum Covers
Coordinates and graphs is a sub-strand under Geometry in the Kenya Institute of Curriculum Development’s Grade 8 Mathematics design. Learners draw a labelled Cartesian plane, identify and plot points, generate a table of values for a linear equation, choose an appropriate scale, draw linear graphs, and solve simultaneous linear equations graphically. The design is listed on the KICD Grade Eight curriculum designs page.
The Cartesian Plane
Two number lines cross at right angles at the origin (0, 0). The horizontal one is the x-axis and the vertical one is the y-axis. A point is written (x, y): go across first, then up or down. This convention is the same one used in OpenStax Prealgebra’s section on the rectangular coordinate system.
- (3, 2): 3 right, 2 up.
- (−4, 1): 4 left, 1 up.
- (0, −3): on the y-axis, 3 down.
Swapping the order is the most common mistake: (2, 3) and (3, 2) are different points. Remember “along the corridor, then up the stairs”.
Table of Values for a Linear Equation
Choose some x-values, substitute them, and record y. For y = 2x + 1:
| x | −1 | 0 | 1 | 2 | 3 |
|---|---|---|---|---|---|
| y | −1 | 1 | 3 | 5 | 7 |
Three points are enough for a straight line; the third acts as a check. If one point does not line up, recheck its calculation.
Choosing a Scale
Look at the smallest and largest values in your table, then pick a scale that fits the graph paper and uses most of the space. Common scales are 1 cm to 1 unit, 1 cm to 2 units, or 2 cm to 1 unit. The two axes may use different scales, but each axis must be evenly spaced. State the scale on your graph.
Drawing a Linear Graph
- Draw and label both axes, with the scale.
- Plot each point from the table neatly with a small cross or dot.
- Join the points with a ruler and extend the line across the grid.
- Label the line with its equation.
Every point on the line satisfies the equation, as explained in OpenStax Prealgebra’s section on graphing linear equations.
Solving Simultaneous Equations Graphically
Two linear equations in x and y are simultaneous when both must be true at once. Draw both lines on the same axes; the point where they meet is the solution, the method shown in OpenStax Elementary Algebra’s section on solving systems by graphing.
Worked example
Solve y = x + 1 and x + y = 5.
- Table for y = x + 1: (0, 1), (1, 2), (3, 4).
- Table for x + y = 5: (0, 5), (2, 3), (5, 0).
- Plot both lines. They cross at (2, 3).
- Check: 3 = 2 + 1 ✓ and 2 + 3 = 5 ✓. So x = 2, y = 3.
Real-life example
In this made-up example, two learners buy pens and books. Akinyi pays KSh 120 for 1 book and 2 pens; Baraka pays KSh 100 for 1 book and 1 pen. Let b be a book’s price and p a pen’s price: b + 2p = 120 and b + p = 100. Graphing both lines (for example with p across and b up) shows they cross at p = 20, b = 80: a pen costs KSh 20 and a book KSh 80.
A graph gives an exact answer only if the crossing point lands on grid lines; otherwise read it as accurately as you can and say it is an estimate.
Original Practice Questions With Worked Answers
- In which quadrant is (−3, −5)? The third quadrant (both negative).
- Complete the table for y = 3x − 2 at x = 0, 1, 2. −2, 1, 4.
- Does (4, 9) lie on y = 2x + 1? 2(4) + 1 = 9, yes.
- The lines y = 2x and y = x + 3 cross at which point? 2x = x + 3, so x = 3, y = 6: (3, 6).
- Values of y range from −6 to 14 and your paper is 12 cm tall. Suggest a y-scale. 1 cm to 2 units (20 units needs 10 cm).
Cover the answers and attempt each question first. For timed practice, use the Grade 8 revision papers or the Grade 8 CBC Challenge. These notes are free; full revision access is available with the KSh 20 Day Pass or the KSh 500 Monthly Pass.
Frequently Asked Questions
How do you plot a point on the Cartesian plane?
Start at the origin, move along the x-axis by the first number, then up or down by the second number.
How many points do I need to draw a straight line?
Two points are enough, but use three so that the third can check your working.
How do you solve simultaneous equations graphically?
Draw both lines on the same axes using tables of values. The coordinates of the point where they cross are the solution.
How do I choose a scale for a graph?
Find the range of values on each axis and pick an even spacing that fits the paper and uses most of it.