Question

Select all of the following points that lie on the graph of f(x) = 7 - 3x.

Answer 1

The points that lie on the graph of f(x) = 7 - 3 x, are (-1 , 10) , (2 , 1)

and (0 , 7)

Step-by-step explanation:

To prove that a point lies on the graph of a line

• Substitute the coordinates of the point in the equation of the line
• If the left hand side is equal to the right hand side, then the point lies on the graph of the line

∵ The equation of the line is f(x) = 7 - 3 x

∵ f(x) = y

∴ y = 7 - 3 x

Point (-2 , 1)

∵ x = -2 and y = 1

- Substitute them in the equation

∴ 1 = 7 - 3(-2)

∴ 1 = 7 + 6

∴ 1 ≠ 13

∵ The left hand side is not equal the right hand side

∴ Point (-2 , 1) does not lie on the graph of the line

Point (-1 , 10)

∵ x = -1 and y = 10

- Substitute them in the equation

∴ 10 = 7 - 3(-1)

∴ 10 = 7 + 3

∴ 10 = 10

∵ The left hand side is equal the right hand side

∴ Point (-1 , 10) lies on the graph of the line

Point (2 , 1)

∵ x = 2 and y = 1

- Substitute them in the equation

∴ 1 = 7 - 3(2)

∴ 1 = 7 - 6

∴ 1 = 1

∵ The left hand side is equal the right hand side

∴ Point (2 , 1) lies on the graph of the line

Point (1 , 5)

∵ x = 1 and y = 5

- Substitute them in the equation

∴ 5 = 7 - 3(1)

∴ 5 = 7 - 3

∴ 5 ≠ 4

∵ The left hand side is not equal the right hand side

∴ Point (1 , 5) does not lie on the graph of the line

Point (0 , 7)

∵ x = 0 and y = 7

- Substitute them in the equation

∴ 7 = 7 - 3(0)

∴ 7 = 7 - 0

∴ 7 = 7

∵ The left hand side is equal the right hand side

∴ Point (0 , 7) lies on the graph of the line

The points that lie on the graph of f(x) = 7 - 3 x, are (-1 , 10) , (2 , 1)

and (0 , 7)

Learn more:

You can learn more about the linear equation in brainly.com/question/4326955

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