Final answer:
Changing the slope of a look-up table (LUT) graph will affect the tilt of the line, with increases resulting in a steeper upward tilt or a steeper downward tilt if negative, and decreases making the line flatter. The greater the absolute value of the slope, the steeper the line. Adjustments to the slope influence the graphical representation of relationships, such as the trade-offs in a labor-leisure diagram.
Step-by-step explanation:
Changing the slope of a look-up table (LUT) graph will affect the tilt of a line on a graph. Increasing the slope of a line that is neither horizontal nor vertical and has a positive slope will result in the line rotating counterclockwise around the y-intercept. Conversely, decreasing the slope will make the line flatter, rotating it clockwise around the y-intercept, if we are starting from a positive slope. It is important to understand that these changes in the slope, whether increased or decreased, will alter the steepness of the line without affecting the y-intercept unless specified.
For example, in the labor-leisure diagram, an increase in slope indicates a higher wage rate; it shows that with higher wages, Petunia will consume less leisure and more income, demonstrating the substitution effect. The slope of the line reflects important information depending upon its application, such as the trade-off between two options, the rate of change, or the steepness of an increase or decrease as seen on graphs.