To plot an ordered pair, read the horizontal coordinate first and the vertical coordinate second. For example, (2, 3) means move 2 units right from the origin, then 3 units up. The numbers describe distances in units, so check the scale before counting squares.
These Grade 8 coordinates and graphs worked examples cover plotting and reading points, choosing scales, correcting misleading axes, and drawing a straight-line graph from a table. The questions and data are original revision practice, with fully explained answers.
Where this topic fits
KICD’s Grade 8 Mathematics design places Coordinates and Graphs in Geometry, sub-strand 4.2. Its outcomes include locating points, generating tables for linear equations, choosing scales and drawing linear graphs. This guide concentrates on those foundations; it does not cover every outcome in the sub-strand. Teachers can consult the Mathematics design on the official KICD Grade Eight Designs page.
1. Understand the axes, origin and ordered pairs
A Cartesian plane has two perpendicular number lines. The horizontal number line is the x-axis; the vertical one is the y-axis. They meet at the origin, whose coordinates are (0, 0). Positive x-values go right, negative x-values go left, positive y-values go up, and negative y-values go down.
An ordered pair is written (x, y). The order matters: (2, 3) and (3, 2) normally identify different points. A helpful routine is “across, then up or down”. Move along the x-direction first, then move parallel to the y-axis.
- (−3, 1): 3 units left, then 1 unit up.
- (−2, −2): 2 units left, then 2 units down.
- (0, 2): no horizontal movement; the point is on the y-axis.
- (2, 0): no vertical movement; the point is on the x-axis.
The axes divide the plane into four quadrants. Starting at the top right and moving anticlockwise, the signs are (+, +), (−, +), (−, −) and (+, −). A point on an axis is not inside a quadrant. You can locate a point correctly from its signs even before counting its exact position.
2. Read and plot an original set of coordinates
Imagine these points as labelled markers on a classroom floor plan. Each coordinate unit represents one equal step on the plan, not a measured metre. Use one square for one unit on both axes.
| Marker | Coordinates (x, y) | Location |
|---|---|---|
| A | (2, 3) | Top-right quadrant |
| B | (−3, 1) | Top-left quadrant |
| C | (−2, −2) | Bottom-left quadrant |
| D | (3, −1) | Bottom-right quadrant |
| E | (0, 2) | On the y-axis |
| F | (2, 0) | On the x-axis |
The table plot below is a text-readable coordinate diagram. Columns show x-values from left to right; rows show y-values from top to bottom. Each dot means there is no labelled marker at that position. O marks the origin. The x = 0 column and y = 0 row represent the axes.
| y / x | −3 | −2 | −1 | 0 | 1 | 2 | 3 |
|---|---|---|---|---|---|---|---|
| 3 | · | · | · | · | · | A | · |
| 2 | · | · | · | E | · | · | · |
| 1 | B | · | · | · | · | · | · |
| 0 | · | · | · | O | · | F | · |
| −1 | · | · | · | · | · | · | D |
| −2 | · | C | · | · | · | · | · |
| −3 | · | · | · | · | · | · | · |
Text alternative: A is at x = 2, y = 3; B at x = −3, y = 1; C at x = −2, y = −2; D at x = 3, y = −1; E at x = 0, y = 2; F at x = 2, y = 0. O is at x = 0, y = 0. The browser’s cell widths are not a physical measurement scale; copy the values onto equal squares when drawing on paper.
Worked reading: find B
Start at B and trace its column to the x-label: −3. Its row has y-label 1. Therefore B is (−3, 1), not (1, −3). To check, begin at O, move three coordinate intervals left and one up. You reach B.
Worked plotting: add G(−1, 3)
From the origin, move one unit left. Stay at x = −1 and move three units up. Put a small cross in the row y = 3, column x = −1, and write G beside it. A large dot covering several intersections makes the intended coordinate harder to read.
3. Choose a scale that fits the values
A scale states what an equal spacing represents. If one square represents 2 units, four squares represent 8 units. A sensible scale uses a useful portion of the graph paper, accommodates all the data and makes values straightforward to plot.
Suppose an original exercise gives the pairs (0, 0), (1, 5), (2, 10), (3, 15), (4, 20) and (5, 25). You have ten squares horizontally and ten vertically. One square for one unit on both axes would leave insufficient vertical space.
- Use 2 squares for 1 x-unit. The range 0 to 5 then occupies ten squares.
- Use 1 square for 5 y-units. The range 0 to 25 occupies five squares.
- Label the x-axis 0, 1, 2, 3, 4, 5 at every second square.
- Label the y-axis 0, 5, 10, 15, 20, 25 at successive squares.
The two axes may use different scales. What must stay constant is the scale along each individual axis. To plot (3, 15) here, move six squares right and three squares up. Its coordinates remain (3, 15); they do not become (6, 3).
For data with named quantities, label those quantities and their units too, such as “Time (min)” and “Volume (mL)”. For a pure equation exercise, x and y labels are sufficient unless the question gives a context.
4. Correct a deliberately wrong graph
A learner draws equally spaced vertical marks and labels them 0, 2, 4, 8, 10. They put a point at the third mark above zero and call its y-coordinate 8. They also write (1, 1) at the crossing of the two zero-labelled axes.
First correction: restore equal numerical intervals. With equal physical spacing and a step of 2, the labels must be 0, 2, 4, 6, 8, 10. The jump from 4 to 8 is twice the other jumps, so the original labelling is inconsistent. The third equal interval above zero represents 6, not 8.
Second correction: fix the origin. Where x = 0 and y = 0 meet, the coordinate is (0, 0). The point (1, 1) belongs one unit right and one unit up, using the chosen scales. Writing a different pair at the crossing does not move the true origin.
Third correction: replot from the source data. If the intended point is (2, 8), keep x = 2 and place it four vertical intervals above zero on the corrected scale. Do not merely relabel the axis and assume every existing point is still correctly placed.
A graph may sometimes show only part of a much larger range, but omitted values must be made clear. For these beginning Cartesian exercises, show the zero positions and use unbroken, evenly spaced scales. That makes the origin and signs easy to check.
5. Build a table and draw a linear graph
Consider the equation y = 2x + 2 for x-values from 0 to 4. A table helps you calculate points before drawing. Substitute each x-value into the same rule, carrying out multiplication before addition.
| x | Calculation | y | Point |
|---|---|---|---|
| 0 | 2 × 0 + 2 | 2 | (0, 2) |
| 1 | 2 × 1 + 2 | 4 | (1, 4) |
| 2 | 2 × 2 + 2 | 6 | (2, 6) |
| 3 | 2 × 3 + 2 | 8 | (3, 8) |
| 4 | 2 × 4 + 2 | 10 | (4, 10) |
Draw axes covering x = 0 to 4 and y = 0 to 10. Choose one square for one x-unit and one square for two y-units. Plot the five points. They should lie on one straight line. Use a ruler to draw the line through them over the requested interval, and label it y = 2x + 2.
Check the point between entries: at x = 2.5, the line gives y = 7. Substitution confirms this: 2 × 2.5 + 2 = 7. The equation describes a continuous line, so values between the table entries are meaningful. The table is a selection of points on that line.
Do not join every unrelated collection of points simply because it is on a grid. The six floor-plan markers earlier represent separate positions. A straight-line equation provides a reason for joining its plotted points; an arbitrary set of locations does not.
6. Three practice questions with worked answers
Practice 1: signs and order
Question: Plot P(−2, 3), Q(3, −2) and R(0, −3). Which point lies on an axis? A learner says P and Q are the same because they contain the same numbers. Explain the error.
Answer: P is two units left and three up. Q is three right and two down. R lies on the y-axis, three units below the origin, because its x-coordinate is zero. P and Q are different: both the order and the signs tell us which direction to move. P has negative x and positive y, while Q has positive x and negative y.
Practice 2: squares versus coordinate values
Question: On a graph, one horizontal square represents 2 units and one vertical square represents 5 units. S is three squares left of the origin and two squares above it. Find S. How many squares are needed to plot T(4, −15)?
Answer: For S, x = −3 × 2 = −6 and y = 2 × 5 = 10, giving S(−6, 10). For T, 4 ÷ 2 = 2 horizontal squares to the right; 15 ÷ 5 = 3 vertical squares down. Always state the coordinate pair in units, rather than reporting the number of squares.
Practice 3: table, line and a check
Question: Complete the table for y = 3x − 1 when x = −1, 0, 1 and 2. Does the point (2, 6) lie on the line?
Answer: The y-values are −4, −1, 2 and 5. For example, when x = −1, y = 3 × (−1) − 1 = −4. Plot (−1, −4), (0, −1), (1, 2) and (2, 5), then draw the straight line through them. The point (2, 6) is not on this line: substituting x = 2 gives y = 5. A point must satisfy the equation, not merely look close on a small drawing.
Compare two displays of one fictional class survey
Coordinate plotting locates points. A survey display must also preserve categories, frequencies and comparison meaning. The example below is an invented set of 20 anonymous responses, not data collected from real children. The question is “Which one of these four classroom activities would you choose?” Every fictional respondent chooses exactly one: Reading (R), Drawing (D), Music (M) or Games (G). These are categories, not measured numerical coordinates.
Complete response record and frequency check
Responses in recording order: R, D, M, G, R, D, M, G, R, D, M, G, R, D, M, R, D, R, D, R.
| Activity | Frequency (responses) | Fraction of total | Percentage |
|---|---|---|---|
| Reading | 7 | 7/20 | 35% |
| Drawing | 6 | 6/20 | 30% |
| Music | 4 | 4/20 | 20% |
| Games | 3 | 3/20 | 15% |
| Total | 20 | 20/20 | 100% |
Count the source record once for each code. The frequencies sum to 7 + 6 + 4 + 3 = 20, matching the number of responses. The modal category is Reading. Averaging the category codes would have no useful meaning.
Worked comparison: the values agree, but the bar lengths mislead
Display A uses a zero baseline. Display B shows the same four values with its vertical axis starting at 2. Both use equally spaced ticks, equal-width bars, the same category order and the unit “responses”. The labelled baseline of B is deliberate so you can diagnose its effect.
Reading has 7 responses and Games has 3, so Reading has 4 more and 7/3 ≈ 2.33 times as many. In A, bar lengths represent 7 and 3 units. In B, visible lengths represent 7 − 2 = 5 and 3 − 2 = 1 units, creating an apparent five-to-one comparison. B’s written numbers are accurate, but its lengths exaggerate this comparison. Choose A for comparing category counts.
This applies the zero-baseline and category-choice reasoning used in the prepared chart-choice lesson. A line connecting R, D, M and G would imply a meaningful sequence absent from the question. A correctly labelled pie chart with sectors 126°, 108°, 72° and 54° would also represent these shares; a bar chart makes the close 7-versus-6 comparison easier to read. No display establishes preferences outside this invented class or explains why any choice was made.
Independent display repair
For the same response record, a third designer truncates the count axis at 1 and claims “Reading is three times as popular as Games” by comparing visible bars. Check the claim, specify a fair bar chart and write one supported comparison plus one limit. Then find the fraction choosing Drawing or Music.
Sample answer and review guide
The visible lengths would be 7 − 1 = 6 and 3 − 1 = 2, hence the misleading factor 3. The actual ratio remains 7:3, not 3:1. Redraw with a zero count baseline, equal increments, equal bar widths and gaps, title, category labels and “responses” on the count axis; plot heights 7, 6, 4, 3. A supported statement is “Reading received one more response than Drawing.” A limit is “These invented responses cannot establish what other classes prefer.” Drawing or Music accounts for (6 + 4)/20 = 1/2 = 50%.
Review the task against four checks: source record reconciled with total 20; all four categories retained; visual quantities compared against the actual counts; and conclusion restricted to the supplied data. Equivalent accurate comparisons are valid. A more attractive colour palette does not repair a distorted baseline.
Frequently asked questions
What is the correct order for coordinates?
Write (x, y): horizontal value first, vertical value second. Include brackets, a comma and any negative signs.
What are the coordinates of the origin?
The origin is (0, 0), where the x-axis and y-axis meet at their zero values.
Can the two axes use different scales?
Yes. For example, one horizontal square may represent 1 unit while one vertical square represents 2 units. Keep each axis internally consistent and label it clearly.
Does a point with zero belong to a quadrant?
If either coordinate is zero, the point is on an axis rather than inside a quadrant. If both are zero, it is the origin.
How do I plot a negative coordinate?
A negative x-value means move left from zero. A negative y-value means move down. Apply these directions separately to the two numbers.
Why are my straight-line graph points not lining up?
Recheck substitution, negative signs, the coordinate order and the scale. One incorrect table entry or one misplaced point can interrupt the pattern.
Should I join all the points I plot?
No. Join points when the task or mathematical relationship calls for it. Use a straight line for a linear equation; leave unrelated location markers as separate points.
Can I use these questions as official past-paper answers?
No. These are original practice questions with worked solutions. They are not labelled as official examination questions or a marking scheme.
Continue practising
First redraw the floor-plan points without looking at the answers. Then explain your scales aloud before drawing either equation. If you need broader resources, see the Grade 8 Mathematics notes resource page. For older practice sets, the 2026 Grade 8 examination directory is a separate, login-gated collection. Its public page does not establish which individual papers or answers are available.
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