Question

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 determine the equation described in the table, we can analyze the relationship between \( x \) and \( y \).

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

We can see that as \( x \) increases by 1, \( y \) increases by 1 as well. This indicates that the function is linear.

We can express this relationship in the slope-intercept form of a linear equation, which is \( y = mx + b \), where \( m \) is the slope and \( b \) is the y-intercept.

1. The slope \( m \) is the change in \( y \) over the change in \( x \):
- The change in \( y \) is \( -9 - (-10) = 1 \),
- The change in \( x \) is \( 1 - 0 = 1 \).
- Therefore, \( m = \frac{1}{1} = 1 \).

2. To find the y-intercept \( b \), we can use one of the points. Using the point \( (0, -10) \):
- When \( x = 0 \), \( y = -10 \), so \( b = -10 \).

Thus, we can write the equation as:
\[
y = 1x - 10
\]
or simply:
\[
y = x - 10
\]

In function notation, we express \( y \) as \( f(x) \):
\[
f(x) = x - 10
\]

So the answer is:
\[
f(x) = x - 10
\]