The worksheets themselves are in German – just as in class. The editor is only available in German so far.
Linear functions – worksheets to print
Linear functions y = m · x + b: tables of values, reading the equation off a graph, drawing lines, slope from two points, checking whether a point lies on the line, zeros and real-life situations such as a taxi or a phone plan.
- Choose the number of tasks and the difficulty yourself
- With an answer sheet and, if you like, a QR code to the answers
- At three levels (★ to ★★★) and as group A and B
- As a single worksheet or as a task on a mixed worksheet
Linear functions: explained simply
A linear function gives every x exactly one y: y = m · x + b. Its graph is a straight line. m is the slope, b the intercept on the y-axis.
How to work it out
- Slope m = change in y : change in x. If the line rises to the right, m is positive; if it falls, m is negative.
- b is the y-value at x = 0, so the point (0|b) on the y-axis. For y = m · x, b = 0: the line passes through the origin.
- Checking a point: put the x of the point into the equation. If the y of the point comes out, it lies on the line. Zero: set y = 0 and solve for x.
An example, step by step
Draw y = 2 · x − 1 and check whether P(3|5) lies on the line.
- Start at b = −1 on the y-axis: the point (0|−1).
- Slope 2 means: 1 to the right, 2 up. That gives (1|1), (2|3), (3|5).
- Check: 2 · 3 − 1 = 5. P(3|5) lies on the line.
Understand other variations
Slope from two points
For P(1|2) and Q(3|8): m = (8 − 2) : (3 − 1) = 6 : 2 = 3. Then b: 2 = 3 · 1 + b, so b = −1. The equation is y = 3 · x − 1.
Zero
For y = 2 · x − 6 you set y = 0: 2 · x − 6 = 0, so 2 · x = 6 and x = 3. The line crosses the x-axis at (3|0).
Real-life situation
A taxi costs 3 € base fare and 2 € per kilometre: y = 2 · x + 3. The base fare is b, the price per kilometre is the slope m. For 8 km: 2 · 8 + 3 = 19 €.
Your turn
What are the slope and the y-intercept of y = −0.5 · x + 4?
Show the answer and method
m = −0.5: for each step to the right the line goes down 0.5. b = 4: the line crosses the y-axis at (0|4).
Ready-made worksheets: Linear functions
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