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Solved problems for the chapter:

Graphs of linear functions

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Graph of a linear function for KS4

1. y-intercepts

2. Gradients

2.1. Increasing function

2.2. Decreasing function

2.3. Constant function

3. Zero function

4. Drawing the graph of a function

4.1. Drawing points

4.2. Use of y-intercepts and gradients

5. Graph of a function with an absolute value

6. Forum

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Cartesian coordinate system

1. Point in rectangular coordinate system

2. Quadrants

3. Mirroring

3.1. Mirroring across the abscissa axis

3.2. Mirroring across the ordinate axis

3.3. Mirroring over the starting point

4. Sets of points in the plane

5. Forum

↓ Show theory [2] ↓

Detailed solution steps are available at:

https://en.openprof.com/wb/chapter:graphs_of_linear_functions/5256/

Example 1.

We start filling the pool with water. When filling began, the water in the pool had already reached a certain height. The water level increases linearly with time. The figure shows the graph of the function f, which shows the change in the height h of the water in the pool depending on the time t. Answer the questions below. Water height is measured in meters and time in minutes.

What was the height of the water in the pool when it started filling?
What was the height of the water in the pool one hour after it started filling?
How much did the water level in the pool increase every 15 minutes?
Write down the function f.

Example 2.

Determine which pairs of quantities are dependent.

Table length and table width.
Apples weight and price of apples.
Width b of the rectangle and the perimeter of the rectangle.
The length of the sides of the square and the area of the square.

Explain why the following pairs of quantities are dependent.

number of instructors and the amount we pay for all instructors.
the length of the journey from home to school and the time we spend on that journey.

The graph (blue line) shows the dependence of the variable y on the variable x. Write down the value of the variable x when .

We look at a wooden table with a top surface (dining area) in the shape of a circle. Write down pairs of quantities that are dependent.

1. the thickness of the upper surface of the table	a. the height of the drawer that can be stored under the table
2. table height	b. table surface
3. the diameter of the upper surface of the table	c. table mass

Determine which pairs of quantities are not independent.

length a of one side in the rectangle and the perimeter of the rectangle.
The magnitude of the angle in the triangle and the sum of the interior angles in the triangle.
Human height and hair colour.