Question

Write a linear function f with the given values
f(0)=2, f(2)=4

Answer 1

What's the form of y=1x+2 as an answer to that question

Answer 2

To write a linear function \( f(x) \) in the form of \( f(x) = mx + b \), we will use the two given points: \( (0, 2) \) and \( (2, 4) \).

1. **Identifying the slope \( m \)**:
The slope \( m \) can be calculated using the formula:

\[
m = \frac{f(x_2) - f(x_1)}{x_2 - x_1}
\]

Using the points \( (0, 2) \) and \( (2, 4) \):

\[
m = \frac{4 - 2}{2 - 0} = \frac{2}{2} = 1
\]

2. **Using the slope to find the intercept \( b \)**:
We can substitute one of the points into the linear equation to find \( b \). We'll use the point \( (0, 2) \):

\[
f(0) = m \cdot 0 + b = 2
\]

This simplifies to:

\[
b = 2
\]

3. **Writing the final function**:
Now we have \( m = 1 \) and \( b = 2 \). Therefore, the linear function is:

\[
f(x) = 1x + 2 = x + 2
\]

So, the linear function \( f \) that meets the specified conditions is:

\[
f(x) = x + 2
\]

Answer 3

The equation \( y = 1x + 2 \) can be simplified as follows:

1. The coefficient of \( x \) is 1, which can be omitted for simplicity. Thus, we can rewrite it as:

\[
y = x + 2
\]

In this case, the form is still a linear function, and it adheres to the general linear equation format \( y = mx + b \), where:
- \( m \) (the slope) is 1,
- \( b \) (the y-intercept) is 2.

So, in final response to your question, the form of the linear function is:

\[
y = x + 2
\]