Question

Use the table to answer the question.

x y
0 −10

1 −9

2 −8

3 −7

Using function notation, what is the equation described in the table?(1 point)
f(x)=?x+?

Answer 1

To find the equation described in the table, we first notice the change in y values corresponding to the change in x values.

The table data is:

- When \( x = 0 \), \( y = -10 \)
- When \( x = 1 \), \( y = -9 \)
- When \( x = 2 \), \( y = -8 \)
- When \( x = 3 \), \( y = -7 \)

As \( x \) increases by 1, \( y \) increases by 1. This indicates a linear relationship with a slope of 1.

Now let's express this relationship in the slope-intercept form \( y = mx + b \), where \( m \) is the slope and \( b \) is the y-intercept.

From the table:
- The slope \( m = 1 \).
- The y-intercept (when \( x = 0 \)) is \( b = -10 \).

So, the equation is:
\[
y = 1x - 10
\]
In function notation, we can write:
\[
f(x) = x - 10
\]

Thus, the equation described in the table is:
\[
f(x) = x - 10
\]