x y 1 5 2 7 3 9 4 11 The table above shows some pairs of x values and

Question

x y 1 5 2 7 3 9 4 11 The table above shows some pairs of x values and y values. Which of the following equations could represent the relationship between x and y ?

Accepted Answer

Choice A is correct. Each of the choices is a linear equation in the form y = mx + b , where m and b are constants. In this equation, m represents the change in y for each increase in x by 1. From the table, it can be determined that the value of y increases by 2 for each increase in x by 1. In other words, for the pairs of x and y in the given table, m = 2. The value of b can be found by substituting the values of x and y from any row of the table and substituting the value of m into the equation y = mx + b and then solving for b . For example, using x = 1, y = 5, and m = 2 yields 5 = 2(1) + b . Solving for b yields b = 3. Therefore, the equation y = 2 x + 3 could represent the relationship between x and y in the given table. Alternatively, if an equation represents the relationship between x and y , then when each pair of x and y from the table is substituted into the equation, the result will be a true statement. Of the equations given, the equation y = 2 x + 3 in choice A is the only equation that results in a true statement when each of the pairs of x and y are substituted into the equation. Choices B, C, and D are incorrect because when at least one pair of x and y from the table is substituted into the equations given in these choices, the result is a false statement. For example, when the pair x = 4 and y = 11 is substituted into the equation in choice B, the result is 11 = 3(4) - 2, or 11 = 10, which is false.

Question x-y-1-