Linear functions - Determining equations.
Test Yourself 1.
Where no diagram has been provided by the cruel person writing these questions,
draw your own set of axes so you can get a feeling for the problem and therefore for the equation.
Interpreting basic equations. | 1. What are the x and y intercepts for the line whose equation is y = 3x - 2? | ||||||||||||
2. What are the x and y intercepts for the line whose equation is y = -2x + 3? | |||||||||||||
3. What are the x and y intercepts for the line whose equation is 2x + 3y - 2 = 0? | |||||||||||||
4. What are the x and y intercepts for the line whose equation is 4x - 5y - 1 = 0? | |||||||||||||
Given 1 point and the gradient (answer in gradient intercept form). |
5. Determine the equation of the line through the point (1,2) with a gradient of 5.
Answer.y = 5x - 3. |
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6. Determine the equation of the line shown in the graph below:
Answer.y = x. |
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7. Determine the equation of the line through the point (-1, -2) with a gradient of -4.
Answer.y = -4x - 6. |
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8. Determine the equation of the line shown in the graph below:
Answer.y = -2x + 2. |
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9. Determine the equation of the line through the point (1, -2) with a gradient of 0.
Answer.y = -2. |
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Given two points (answer in general form). |
10. Determine the equation of the line shown in the graph below:
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11. Determine the equation of the line through the points (10, 3) and (15, 8).
Answer.y = x - 7. |
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12. Determine the equation of the line through the points (-12, 3) and (4, -5) | |||||||||||||
13. Determine the equation of the line through the points (3.5, 2.7) and (5.5, 10.7).
Answer.y = 4x - 11.3. |
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14. Determine the equation of the line through the points (3, -2) and (3, 2).
Answer.x = 3. |
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Given data in a table. | 15. The following table shows data based on a linear relationship between A and B.
Answer.(i) B = 2A -1. (ii) Missing numbers are Y = 29 and X = 48. |
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16. The following table shows data based on a linear relationship between X and Y.
Answer.(i) Y = -4X + 23. (ii) Missing number is X = 14. |
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Given data in a diagram. | 17. What is the equation of the blue line shown in the following diagram? Answer.y = 6 - 2x. | ||||||||||||
18. What is the equation of the blue line shown in the following diagram?
Answer.y = x/3 - 3 or x - 3y - 9 = 0. |
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Given a geometrical context. | 19. What is the equation of the horizontal line passing through the point (-22, 15)?
Answer.y = 15. |
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20. What is the equation of the vertical line passing through the point (26, -26)?
Answer.x = 26. |
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21. A is the point (2, 3) and the point C lies on the y axis.
The equation of the line AC is 3x - y - 9 = 0. Given ABCD is a rectangle, determine the coordinates of the points B and D. Answer.B is (0, 3) and D is (2, -9). |
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22. The vertex of the isosceles triangle ABC is the point A with coordinates (3, 4). B is the point (0, 7) and the base of the triangle lies along the y axis.
Draw a sketch showing this information and hence find the coordinates of point C. Answer.C is (0, 1). |
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Applications to the physical world. | 23. Ish starts to save her money in a special holiday account. She begins by depositing $500 and then deposits $40 each week from her part time job.
Answer.Ish saves $1,540 after 26 weeks. |
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24. A car is stationary at a given time. It then moves and increases its speed at a constant rate of 0.4 metres/second.
Answer.It takes 41.75 secs. |
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25. The average height, C, in centimetres, of a girl between the ages of 6 years and 11 years can be represented by a line with the equation C = 6A + 79 where A is the age of a girl in years.
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