Straight-line Graphs

Overview

Lesson 4 of 6 focuses on plotting and sketching graphs for equations that represent straight-line relationships. Students apply coordinate plane skills to connect equation features to graph features, building the foundations needed for later quadratic modelling.

Learning intentions

• Students will graph linear equations on the Cartesian plane by plotting points and drawing accurate lines.
• Students will identify and interpret the gradient (slope) and y-intercept from a linear equation.
• Students will check the reasonableness of their graphs by comparing predicted points to their drawn line.
• Students will use digital tools to test how changing a linear equation changes its graph.

Success criteria

• I can plot two or more correct points from an equation.
• I can draw the straight line through the plotted points accurately.
• I can state the y-intercept from the equation and locate it on the graph.
• I can state the gradient from the equation and explain how it matches the line’s steepness/direction.

Curriculum links

• Algebra — use tables, graphs, and digital tools to identify and graph functions and solve equations graphically and numerically.
• Algebra — interpret features of graphs (such as intercepts and key values) and determine when values lie within a range using graphing tools.
• (This lesson supports later work in solving equations graphically and comparing numerical solutions to graphical solutions.)

Lesson structure (45 minutes)

1. 0–5 min · Hook (Green School entry). Teacher shows a prepared graph with a clearly marked intercept and asks: “What equation might produce this line?” Students do a quick think-pair-share, naming any visible features (y-intercept/steepness).

2. 5–12 min · Direct teach: reading an equation as a graph. Teacher models converting a linear rule into points: choose two x-values, compute y, then plot and join with a straight line. Students copy a worked example step-by-step (e.g., for (y=2x+3): use (x=0) and (x=1), plot ((0,3)) and ((1,5)), then draw).

3. 12–22 min · Guided practice: plot points and draw lines. Teacher assigns 3 linear equations (set of mixed difficulty) and demonstrates accuracy checks: use the gradient as “rise/run” and confirm the y-intercept is where the line crosses the y-axis. Students work in pairs on graph paper (teacher circulates to check point plotting before line drawing). Teacher prompts: “Where is the y-intercept?” “How do you know the gradient matches your line?”

4. 22–30 min · Accuracy check stations (rapid cycles). Teacher sets up two mini-stations: Station A for manual graphs, Station B for quick digital plotting. Students rotate:

• Station A: redraw one graph more carefully using ruler to reduce wobble.
• Station B: in graphing software, enter the equation and compare the plotted line to their manual graph.

5. 30–38 min · Independent task: slope and intercept from the equation. Teacher provides 4 equations; for each, students state gradient and y-intercept, then graph from two points. Students complete independently, using colour-coded labels (e.g., gradient marked in one colour, y-intercept in another).

6. 38–45 min · Exit ticket + teacher feedback. Teacher collects: one completed graph and two short written answers (gradient and y-intercept for a new equation). Students submit; teacher does immediate next-lesson sorting of common errors (wrong axis value, swapped gradient sign, line not straight).

Resources

• Graph paper (including some pre-marked axes for support)
• Rulers, coloured pens (e.g., blue for y-intercept, red for gradient/rise-run)
• Pre-printed plotting templates with numbered steps
• Worked examples sheet (one per pair)
• Graphing software or an online graphing tool on devices
• Equation cards (gradient positive/negative; integer and simple fraction intercepts if appropriate)
• Personal whiteboards or mini-slates for quick checks
• Dyslexia-friendly overlays if available (colour tint) and large-font handouts

Assessment

• Formative: teacher observations during guided practice (correct point plotting before drawing)
• Formative: station comparison (manual vs digital) with a quick “What matches? What differs?”
• Summative-for-now: exit ticket identifying gradient and y-intercept and showing the plotted graph

Differentiation

• Support (additional access):
• Provide pre-marked axes graph paper and a “plot-two-points” worksheet with blanks for coordinates.
• Use sentence starters: “The y-intercept is … because when (x=0), (y=...)” and “The gradient is … because for every increase of 1 in (x), (y) changes by …”
• Offer step-by-step checklists and allow verbal clarification before drawing lines.
• Whole-class access:
• Colour-coded graphs: same colour for the y-intercept point and label; same colour for rise/run markings.
• Use clear ruler-based expectations: “line through both points, straight, no curve.”
• Challenge (advanced students):
• Provide extra equation cards and ask students to predict the graph feature changes without plotting first (e.g., “What happens to the intercept if +5 is added?”).
• Require explanation: “My gradient is negative because the line goes down as x increases.”
• Extension (technology and real-life data; advanced learners):
• Students conduct a short class survey (e.g., minutes vs task score, or device usage vs screen-on time category converted to numbers).
• Convert results into a linear model where appropriate, graph using digital tools, and write a short interpretation: gradient meaning and y-intercept meaning in context.

Dyslexia-friendly reading options

• Provide key instructions in short bullet form with large font and generous spacing.
• Read aloud the step instructions (or provide an audio recording of the worksheet directions).
• Use colour-coding to separate: equation parts (rule), point plotting, and gradient/intercept labels.
• Allow students to use a “highlight and point” method (highlight the y-intercept, underline rise/run, then plot).