Math Problem Statement

The equation y=4x represents the relationship between the gallons of water in a bathtub (y) and the number of minutes (x) the water runs out.

If this relationship is represented on a graph, which coordinate pair would NOT be on the line?

Responses

(5,20) (5,20)

(1,4) (1,4)

(4,12) (4,12)

(2,8) (2,8)

Solution

To determine which coordinate pair would NOT lie on the line represented by the equation y=4xy = 4x, substitute each xx value into the equation and verify whether the resulting yy value matches the pair.

Steps:

  1. The equation is y=4xy = 4x, meaning yy is four times xx.

  2. Check each pair:

    • (5,20)(5, 20): Substitute x=5x = 5 into y=4xy = 4x: y=4(5)=20y = 4(5) = 20 Matches (5,20)(5, 20), so this is on the line.

    • (1,4)(1, 4): Substitute x=1x = 1 into y=4xy = 4x: y=4(1)=4y = 4(1) = 4 Matches (1,4)(1, 4), so this is on the line.

    • (4,12)(4, 12): Substitute x=4x = 4 into y=4xy = 4x: y=4(4)=16y = 4(4) = 16 Does not match (4,12)(4, 12). This pair is NOT on the line.

    • (2,8)(2, 8): Substitute x=2x = 2 into y=4xy = 4x: y=4(2)=8y = 4(2) = 8 Matches (2,8)(2, 8), so this is on the line.

Conclusion:

The coordinate pair (4,12)(4, 12) would NOT be on the line.


Would you like me to elaborate on graphing this or similar questions?

5 Related Questions:

  1. How can you verify if a point lies on a line using an equation?
  2. What does the slope of y=4xy = 4x represent in a real-world context?
  3. How would the graph change if the equation were y=3x+2y = 3x + 2?
  4. What are the key characteristics of a linear equation like y=4xy = 4x?
  5. How would you find the equation of a line if given two points?

Tip:

When checking if a point is on a line, always substitute the xx-coordinate into the equation to see if the yy-value matches.

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Math Problem Analysis

Mathematical Concepts

Linear Equations
Coordinate Geometry

Formulas

y = 4x

Theorems

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Suitable Grade Level

Grades 6-8