Answer:
The equation of the linear relationship is y = 3x + 2 ⇒ B
Explanation:
To solve the question substitute the x in the equation by the x-coordinate of each point to find y, if y equals the y-coordinate of the point, then the point is on the graph of the equation
A.
∵ y = 2x + 3
→ Use the first point (0, 2)
∵ x = 0
→ Substitute x by 0 in the equation
∴ y = 2(0) + 3
∴ y = 0 + 3 = 3
∵ The y-coordinate is 2
∴ The point (0, 2) does not lie on the graph of the relationship
∴ The equation y = 2x + 3 doesn't represent the equation of the relationship
B.
∵ y = 3x + 2
→ Use the first point (0, 2)
∵ x = 0
→ Substitute x by 0 in the equation
∴ y = 3(0) + 2
∴ y = 0 + 2 = 2
∵ The y-coordinate is 2
∴ The point (0, 2) lies on the graph of the relationship
→ Use the second point (1, 5)
∵ x = 1
→ Substitute x by 1 in the equation
∴ y = 3(1) + 2
∴ y = 3 + 2 = 5
∵ The y-coordinate is 5
∴ The point (1, 5) lies on the graph of the relationship
→ Use the third point (3, 11)
∵ x = 3
→ Substitute x by 3 in the equation
∴ y = 3(3) + 2
∴ y = 9 + 2 = 11
∵ The y-coordinate is 11
∴ The point (3, 11) lies on the graph of the relationship
→ Use the fourth point (2, 7)
∵ x = 2
→ Substitute x by 2 in the equation
∴ y = 3(2) + 2
∴ y = 6 + 2 = 8
∵ The y-coordinate is 7
∴ The point (2, 7) doesn't lie on the graph of the relationship
∴ The equation of the linear relationship is y = 3x + 2