Question

What is the answer for this math problem

Answer 1

The group of all ordered pairs lie on the line is (3, 7), (2, 6), (-2, 2) ⇒ D

Explanation:

To solve this type of question, Form the equation of the line and substitute the x-coordinate of each ordered pair to find y, if the value of y equal to the value of the y-coordinate of the point, then the point is on the line

The form of the linear equation is y = m x + b, where

• m is the slope of the line

• b is the y-intercept (value y at x = 0

• The rule of the slope of the line that passes through points (x1, y1) and (x2, y2) is m =
  `(y2-y1)/(x2-x1)`

From the given figure

∵ The line passes through points (-4, 0) and (0, 4)

∴ x1 = -4 and y1 = 0

∴ x2 = 0 and y2 = 4

→ Substitute them in the rule above

∵ m =
`(4-0)/(0--4)` =
`(4)/(0+4)` =
`(4)/(4)`

∴ m = 1

∵ b is the value of y at x = 0

∵ y = 4 at x = 0

∴ b = 4

→ Substitute the values of m and b in the form of the equation above

∴ y = 1(x) + 4

∴ y = x + 4 ⇒ equation of the given line

Let us check every group

∵ The ordered pairs are (7, 3), (6, 2), (2, -2)

∵ y = x + 4

∵ x = 7

∵ y = 7 + 4 = 11

∵ y-coordinate = 3

∴ Point (7, 3) doesn't lie on the line

∵ The ordered pairs are (5, 1), (3, 7), (2, 6)

∵ x = 5

∴ y = 5 + 4 = 9

∵ y-coordinate = 1

∴ Point (5, 1) doesn't lie on the line

∵ The ordered pairs are (3, 7), (2, 6), (2, 2)

∵ x = 3

∴ y = 3 + 4 = 7

∵ y-coordinate = 7

∴ Point (3, 7) lies on the line

∵ x = 2

∴ y = 2 + 4 = 6

∵ y-coordinate = 6

∴ Point (2, 6) lies on the line

∵ x = 2

∴ y = 6

∵ y-coordinate = 2

∴ Point (2, 2) doesn't lie on the line

∵ The ordered pairs are (3, 7), (2, 6), (-2, 2)

∵ x = 3

∴ y = 3 + 4 = 7

∵ y-coordinate = 7

∴ Point (3, 7) lies on the line

∵ x = 2

∴ y = 2 + 4 = 6

∵ y-coordinate = 6

∴ Point (2, 6) lies on the line

∵ x = -2

∴ y = -2 + 4 = 2

∵ y-coordinate = 2

∴ Point (-2, 2) lies on the line

∵ The three ordered pairs lie on the line

∴ The group of all ordered pairs lie on the line is (3, 7), (2, 6), (-2, 2)

∵ The ordered pairs are (1, 5), (-6, 2), (-7, -3)

∵ x = 1

∴ y = 1 + 4 = 5

∵ y-coordinate = 5

∴ Point (1, 5) lies on the line

∵ x = -6

∴ y = -6 + 4 = -2

∵ y-coordinate = 2

∴ Point (-6, 2) doesn't lie on the line