ALGEBRA & COORDINATE GEOMETRY · INVESTIGATION 01

Linear Function Explorer

Investigate how slope and intercept transform a straight-line graph. Manipulate variables, collect evidence, test mathematical conjectures and explain what the graph reveals.

Guided discoveryLive graphingPractical recordAssessment

Student nameClass / sectionRoll numberExperiment date

03 · Investigation workspace

Interactive coordinate plane

Drag the probe point or use the x slider

The green line represents y = mx + c. The yellow point is the selected ordered pair. Click the graph to move the probe horizontally.

Function ruley = 2x + 1

Selected point(2, 5)

Gradient2

Y-intercept1

Positive slope: the line rises from left to right. The y-intercept is where it crosses the vertical axis.

Mathematical idea

A linear function has the form y = mx + c. The coefficient m is the slope (rate of change), and c is the y-intercept. For every unit increase in x, y changes by m units.

m = (y₂ − y₁) / (x₂ − x₁) and y = mx + c

Aim and procedure

Set an initial slope and intercept. Predict how the line will appear.

Change only the slope. Record the direction and steepness of the line.

Restore the slope and change the intercept. Observe the vertical shift.

Select at least three x-values and calculate corresponding y-values.

Compare your observations with the equation and write a conclusion.

Variables

Independentm or c

DependentGraph / y

ControlledOther value

RelationshipLinear

Fair-test rule: change one parameter at a time while keeping the other parameter fixed.

Live mathematical analysis

Rate of change2

x-intercept−0.5

Angle to +x axis63.4°

Value at x = 01

At x = 2: y = 2 × 2 + 1 = 5

Value table

x	Calculation	y	Ordered pair

The slope gives the change in y for each one-unit increase in x.

Digital practical notebook

Hypothesis – what do you predict?

Observations – what did you notice?

Conclusion – what mathematical rule did you discover?

Possible source of error / limitation

#	Equation	Probe point	Recorded y	Time

Your saved trials will appear here.

Knowledge check

Answer all five questions. Feedback is provided after each response.

Assessment score0 / 5

Investigation challenge

Challenge A: Create a horizontal line that crosses the y-axis at 4.

Challenge B: Create a line with negative gradient passing through (0, −3).

Challenge C: Find a line for which y = 0 when x = 3.