Question

Which equation has all the following points in its solution set? (2,7) (1,5) (5,13) (7,17)

a) y = x
b) y = x + 12
c) y = 2x + 3
d) y = 4x - 3

Answer 1

To determine which equation has all the given points in its solution set, substitute the x and y values of each point into the equations and see which equation satisfies all the points. The equation that satisfies all the given points is y = x + 12.

Step-by-step explanation:

In order to determine which equation has all the given points in its solution set, we can substitute the x and y values of each point into the equations and see which equation satisfies all the points. Let's check each equation one by one:

a) y = x: For each point, substituting the x and y values, we get:

(2,7) --> 7 = 2
(1,5) --> 5 = 1
(5,13) --> 13 = 5
(7,17) --> 17 = 7

From the above results, it is clear that the equation y = x does not satisfy any of the given points. Therefore, option a) is incorrect.

Now let's check option b).

b) y = x + 12: Substituting the x and y values from each point, we get:

(2,7) --> 7 = 2 + 12
(1,5) --> 5 = 1 + 12
(5,13) --> 13 = 5 + 12
(7,17) --> 17 = 7 + 12

From the above results, it is clear that the equation y = x + 12 satisfies all the given points. Therefore, option b) is the correct answer.