Answer:
The equation of the line is y = 2x - 5 ⇒ D
Explanation:
The form of the linear equation is y = m x + b, where
Note: To prove that a line passes through a given point, substitute x in the equation of the line by the x-coordinate of the point and solve to find y, if y equals the y-coordinate of the point, then the line passes through it
∵ The slope of the line is 2
∵ The line passes through the point (3, 1)
→ Find at first which equation has slope 2, then check if the line passes
through the point or not using the note above
A.
∵ y = 2x + 5
→ By comparing it with the form of the equation above
∴ m = 2
∴ The line has the same slope
→ Substitute x by 3 to find y
∵ y = 2(3) + 5 = 6 + 5 = 11
∵ y-coordinate of the point = 1
∴ The line does not pass through the point
B.
∵ y = 2x + 1
→ By comparing it with the form of the equation above
∴ m = 2
∴ The line has the same slope
→ Substitute x by 3 to find y
∵ y = 2(3) + 1 = 6 + 1 = 7
∵ y-coordinate of the point = 1
∴ The line does not pass through the point
C.
∵ y = 2x - 1
→ By comparing it with the form of the equation above
∴ m = 2
∴ The line has the same slope
→ Substitute x by 3 to find y
∵ y = 2(3) - 1 = 6 - 1 = 5
∵ y-coordinate of the point = 1
∴ The line does not pass through the point
D.
∵ y = 2x - 5
→ By comparing it with the form of the equation above
∴ m = 2
∴ The line has the same slope
→ Substitute x by 3 to find y
∵ y = 2(3) - 5 = 6 - 5 = 1
∵ y-coordinate of the point = 1
∴ The line passes through the point
∴ The equation of the line is y = 2x - 5