Choose the appropriate graph of the function y = kx, where k > 0.

Analysis:

The function given is $$y = kx$$. This is a linear function that passes through the origin (0, 0).

The condition $$k > 0$$ means that the slope of the line is positive. A positive slope indicates that as $$x$$ increases, $$y$$ also increases. This means the line will rise from left to right.

Graph 1:

• The line passes through the origin.
• As $$x$$ increases (e.g., from 0 to 1), $$y$$ also increases (e.g., from 0 to 1.5). This indicates a positive slope.
• The line rises from left to right.

Graph 2:

• The line passes through the origin.
• As $$x$$ increases (e.g., from 0 to 1), $$y$$ decreases (e.g., from 0 to -1.5). This indicates a negative slope.
• The line falls from left to right.

Graph 3:

• The line passes through the origin.
• As $$x$$ increases (e.g., from 0 to 1), $$y$$ decreases (e.g., from 0 to -1.5). This indicates a negative slope.
• The line falls from left to right.

Based on the condition $$k > 0$$, we need a line with a positive slope that passes through the origin. Graph 1 satisfies these conditions.