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
The lesson
A linear function has the form y = mx + c. 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 only happens when x appears on its own, to the power 1.
y = mx + c always draws a straight line, where m sets the steepness and direction, and c sets the y-intercept.
Watch it
Where it sits
Where this leads
Jobs that lean on this skill. Follow one to see everything it is built on.
8 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.