Linear Function Graphs
Recognise that a linear function produces a straight-line graph, understand the relationship between an equation of the form y = mx + c and its graphical representation, and interpret gradient and y-intercept in context
What a learner can do afterwards
- Explain that changing m in y = mx + c alters the steepness and direction of the line
- Identify the y-intercept of a line from its equation and from its graph
- Determine whether a given equation will produce a straight line or a curve
1 · Read
Your taxi rule made a table and a graph: it started at £2 and rose £1.50 a mile. A rule like that has a name. It is a linear function, written y = mx + c, and every equation written this way makes a straight line when you graph it. The number m is the gradient. It tells you how steep the line is and whether it slopes up or down as x increases. The number c is the y-intercept. It tells you where the line crosses the y-axis, the point where x = 0.
Take y = 2x + 3. Here m = 2 and c = 3. The line crosses the y-axis at 3, and for every step you move right, it climbs up by 2. You could sketch this line just from the equation: start at 3 on the y-axis, then go up 2 and right 1, again and again.
Not every equation makes a straight line. If x is squared, like in y = x² + 1, or if x is under a fraction, like y = 1/x, the graph curves instead. A straight line happens when x is on its own, to the power 1, or when there is no x at all, as in y = 3.
y = mx + c always draws a straight line, where m sets the steepness and direction, and c sets the y-intercept.
The rewritten readings were written for this dataset.
2 · Watch
Take it off screen
Where it sits
Where this leads
Jobs that lean on this skill. Follow one to see everything it is built on.
20 questions wait behind this lesson, each with its answer explained. Every answer feeds the sky: stars light as they are learned, and dim when it is time to come back.