Question

Math help for homework

Answer 1

`f(x)=x+2`

Explanation:

Given parameters:

• f(0) = 2
• f(2) = 4

Therefore, there are two points on the line:

• (0, 2) and (2, 4)

The linear relationship between the x and y values is:

• The y-value is 2 more than the x-value.

`\implies f(x)=x+2`

To prove this algebraically, define the points:

• (x₁, y₁) = (0, 2)
• (x₂, y₂) = (2, 4)

Find the slope of the linear function by substituting the defined points into the slope formula:

`\implies \textsf{slope}\:(m)=(y_2-y_1)/(x_2-x_1)=(4-2)/(2-0)=(2)/(2)=1`

Substitute the found slope and one of the points into the point-slope formula to create a linear function that satisfies the given parameters:

`\implies y-y_1=m(x-x_1)`

`\implies y-2=1(x-0)`

`\implies y-2=x`

`\implies y=x+2`

Hence proving that the linear function is:

`f(x)=x+2`