Question

f (x)= ____ x + _____

x y
O -10
1 -9
2 -8
3 -7

Answer 1

The relationship between \( x \) and \( y \) in the values you provided appears to be linear.

Given the points:
- (0, -10)
- (1, -9)
- (2, -8)
- (3, -7)

We can see that as \( x \) increases by 1, \( y \) increases by 1. This suggests that the slope of the line is 1.

We can express the linear function in the slope-intercept form \( y = mx + b \), where \( m \) is the slope and \( b \) is the y-intercept.

Here, we have:
- Slope \( m = 1 \)
- To find \( b \), we can use one of the points. Using the point (0, -10):

\[
y = mx + b
\]
\[
-10 = 1(0) + b
\]
\[
b = -10
\]

So, the equation of the line is:

\[
y = 1x - 10
\]

This means that:

\[
f(x) = x - 10
\]

Thus, filling in the blanks, we have:

\[
f(x) = x - 10
\]