Questions: Dê a lei de formação das funções afins correspondentes às retas f e g e encontre o ponto de intersecção dessas duas retas.

Solution Steps

To find the equations of the lines \( f \) and \( g \), we need to identify their slopes and y-intercepts from the graph.

For line \( f \):

• The line passes through the points (0, 2) and (1, 3).
• Slope \( m_f = \frac{3 - 2}{1 - 0} = 1 \).
• Y-intercept \( b_f = 2 \).

Thus, the equation of line \( f \) is: \[ y = x + 2 \]

For line \( g \):

• The line passes through the points (0, 2) and (1, 1).
• Slope \( m_g = \frac{1 - 2}{1 - 0} = -1 \).
• Y-intercept \( b_g = 2 \).

Thus, the equation of line \( g \) is: \[ y = -x + 2 \]

To find the intersection point of the lines \( f \) and \( g \), set their equations equal to each other: \[ x + 2 = -x + 2 \]

Combine like terms to solve for \( x \): \[ x + x = 2 - 2 \] \[ 2x = 0 \] \[ x = 0 \]

Substitute \( x = 0 \) back into either equation to find \( y \): \[ y = 0 + 2 \] \[ y = 2 \]

Final Answer