Identify the graphs that represent the given functions.

Analysis:

• The problem asks to match linear functions to their graphical representations.
• We need to analyze the slope and y-intercept of each function and compare them with the provided graphs.

Function 1: \( y = -\frac{3}{5}x + 3 \)

• Slope: \( m = -\frac{3}{5} \) (negative, so the line goes downwards from left to right).
• Y-intercept: \( b = 3 \) (the line crosses the y-axis at 3).
• Looking at the graphs, graph (A) has a negative slope and appears to cross the y-axis at 3.

Function 2: \( y = \frac{1}{5}x + 3 \)

• Slope: \( m = \frac{1}{5} \) (positive, so the line goes upwards from left to right).
• Y-intercept: \( b = 3 \) (the line crosses the y-axis at 3).
• Looking at the graphs, graph (L) has a positive slope and appears to cross the y-axis at 3.

Function 3: \( y = -3x \)

• Slope: \( m = -3 \) (steep negative slope).
• Y-intercept: \( b = 0 \) (the line passes through the origin).
• Looking at the graphs, graph (B) has a steep negative slope and passes through the origin.

Function 4: \( y = 3x \)

• Slope: \( m = 3 \) (steep positive slope).
• Y-intercept: \( b = 0 \) (the line passes through the origin).
• Looking at the graphs, graph (P) has a steep positive slope and passes through the origin.

Final Matching:

• 1 corresponds to A
• 2 corresponds to L
• 3 corresponds to B
• 4 corresponds to P

Answer: 1-A, 2-L, 3-B, 4-P