Question

which function describes this table of values?

x y
10 8
5 4
0 0
-5 -4

a. y = 5/4x
b. y = 4/5x
c. y = -5/4x
d. y = x -2

Answer 1

To identify the function that describes the given table of values, we need to analyze the relationship between \( x \) and \( y \).

From the provided values:

- \( (10, 8) \)
- \( (5, 4) \)
- \( (0, 0) \)
- \( (-5, -4) \)

Let's check the slope \( m \) using two points from the table, say \( (10, 8) \) and \( (0, 0) \):

Using the formula for the slope:
\[
m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{8 - 0}{10 - 0} = \frac{8}{10} = \frac{4}{5}
\]

Now that we have the slope, we can express \( y \) in terms of \( x \):
\[
y = \frac{4}{5}x
\]

Now we can check which option corresponds to this function.

- Option a: \( y = \frac{5}{4}x \)
- Option b: \( y = \frac{4}{5}x \) (this matches!)
- Option c: \( y = -\frac{5}{4}x \)
- Option d: \( y = x - 2 \)

Since option b is \( y = \frac{4}{5}x \), it accurately represents the relationship between \( x \) and \( y \) in the table.

Thus, the correct answer is:

**b. \( y = \frac{4}{5}x \)**