Question

The table below shows the relationship between x, the number of minutes Jackson has been reading, and y, the total number of pages he has read.

Minutes (x) :
10
15
20
25

Total Pages (y) :
5
7.5
10
12.5


Which equation represents the relationship in the table?


A. y = 2x - 15

B. y = x - 5

C. y = 2x

D. y = 0.5x

Answer 1

To determine the equation that represents the relationship in the table, let's analyze the pattern.

Looking at the values of x and y, we can observe that as the number of minutes (x) increases by 5, the total number of pages (y) increases by 2.5. This indicates that the rate of change is constant, or the relationship between x and y is linear.

To find the equation, we need to find the equation of a line that passes through two of the points in the table. Let's choose the points (10, 5) and (20, 10) since they are the easiest to work with.

Using the point-slope formula, y - y₁ = m(x - x₁), where (x₁, y₁) is one of the points and m is the slope:

Using the first point (10, 5):

y - 5 = (2.5/5)(x - 10)
y - 5 = 0.5(x - 10)
y - 5 = 0.5x - 5
y = 0.5x

Using the second point (20, 10):

y - 10 = (2.5/5)(x - 20)
y - 10 = 0.5(x - 20)
y - 10 = 0.5x - 10
y = 0.5x

We can see that both equations yield the same line, y = 0.5x, which represents the relationship between x and y in the table.

Therefore, the correct equation that represents the relationship in the table is:

D. y = 0.5x.