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After solving Grade 8 math problems from pages 71 to 77 in Kite Book 1 - Exercise 4: Graph of linear function y = ax + b (a not equal to 0), students can proficiently solve related problems regarding the graph of linear functions such as determining intersecting lines and parallel lines; drawing graphs of functions,... If encountering difficulties during problem-solving, students can refer to the instructional materials provided by Mytour below.
Grade 8 Kite Book 1 Pages 71, 72, 73. 74, 75, 76, 77 Math Solutions
Exercise 4: Graph of linear function y = ax + b (a not equal to 0)
Grade 8 Kite Book 1 Page 77 Math Solutions
1. Solve problem 1 - Grade 8 Kite Book 1 Page 77
Problem:
Among the following statements, which one is correct, which one is incorrect about the line d as the graph of the function y = ax + b (a ≠0)?
a) The line d intersects the y-axis at a point with an ordinate equal to -b/a
b) The line d intersects the x-axis at a point with an abscissa equal to b
c) The line d intersects the y-axis at a point with an ordinate equal to b
d) The line d intersects the x-axis at a point with an abscissa equal to -b/a
Solution Method:
Apply the definition of the graph of a linear function
Answer:
The correct statement is: b
The incorrect statement is: a and c
2. Solve problem 2 - Kite Grade 8 exercise 1 page 77
Problem:
Identify the intersecting and parallel pairs of lines among the following lines: y = -2x + 5; y = -2x; y = 4x - 1
Solution Method:
Apply the theorem of graphing functions
Answer:
- Intersecting lines: the line y = 4x - 1 intersects the lines y = -2x + 5; y = -2x
- The pairs of parallel lines: y = -2x + 5; y = -2x
3. Solve problem 3 - Kite Grade 8 Exercise 1 page 77
Problem:
Draw the graphs of the following functions:
Solution Method:
Plot the function graph
Answer:
y = 3x passes through the points (0,0) and (1,3)
y = 3x + 4 passes through the points (0,4) and (1,7)
y = (-1/2)x passes through the points (0,0) and (2,1)
y = (-1/2)x + 3 passes through the points (0,3) and (2,5)
4. Solve Exercise 4 - Kite Grade 8 Exercise Book 1 page 77
Problem:
Determine the line y = ax + b (a ≠ 0) with a slope of -1 and passing through point M(1 ; 2). Then, draw the obtained line on the coordinate plane.
Solution Method:
Apply the definition of slope to graph the function
Answer:
Since the line passes through point M(1 ; 2) and has a slope of -1, we have: 2 = (-1) * 1 + b, so b = 3
Therefore, the equation of the line is y = -x + 3, it will pass through another point with coordinates x = 0, y = 3
5. Solve problem 5 - Kite grade 8 workbook page 77
Problem:
a) Draw the line y = 2x - 1 on the coordinate plane.
b) Determine the line y = ax + b (a ≠0) passing through point M(1; 3) and parallel to the line y = 2x - 1. Then, draw the line found on the coordinate plane.
Solution Method:
Based on the definitions, plot the graph of functions.
Answer:
a) Plot the line y = 2x - 1 on the coordinate plane.
The line y = 2x - 1 will pass through the points (0,-1) and (1,1).
b) The line y = ax + b (a ≠ 0) is parallel to the line y = 2x - 1, so the slope a = 2. Moreover, it passes through point M(1; 3), thus we have 3 = 2(1) + b.
b = 1 ; y = 2x + 1.
This line will pass through another point with coordinates x = 0 and y = 1.
6. Solve Exercise 6 - Kite Grade 8 Exercise Book 1 page 77
Problem:
Two straight lines d1; d2 respectively represent the speeds (unit: m/s) of the first object and the second object over time t(s).
a) Comment on the ordinate of intersection of the two lines d1; d2. Then, comment on the initial speeds of the two motions.
b) Between the two lines d1; d2, which line has a greater slope?
c) Which object has a greater speed from the first second onward? Why?
Solution Method:
Observe the graph and apply the definitions of the function graph
Answer:
a) The lines d1 and d2 intersect at a point with an ordinate of 2. Therefore, the initial velocities of both motions are equal and are both 2 m/s.
b) Among the lines d1 and d2, line d2 has a steeper slope, so it has a larger slope coefficient.
c) From the first second onward, the second object has a greater speed.
Above is the guidance on solving exercises for grade 8, pages 71 to 77, Wings of the kite, volume 1 Graphs of linear functions y = ax + b (a ≠ 0). To prepare for the next lesson, you can preview the directions for solving grade 8 exercises, pages 78, 79 of Wings of the Kite, volume 1 - Last exercise of Chapter III. In addition, the section Solving grade 8 exercises, pages 67, 68, 69, 70 of Wings of the Kite, volume 1 - Exercise 3: Linear function y = ax + b (a ≠ 0) will help reinforce the learned knowledge; you can review the answers here. Wish you all the best in studying mathematics.
Explore more resources for Grade 8 Math:
- Grade 8 Math Solutions from Wings of the Kite series
