Participate in this Discussion Forum: Graphing in psychology:

Are you optimistic or pessimistic? Details: In psychology, perspective plays a tremendous role in treatment and decision-making. Is the glass half-full or half-empty? Questions like this can help us determine an individualâ€™s mindset, such as if someone is optimistic or pessimistic. We then might want to explore the relationship between mindset and something like depression. For this discussion, we will set the x-axis to be depression (with a domain from 1.0 to 4.0) and the y-axis to be optimism (with a range from 1.0 to 8.0). The function you have been given that models the relationship between optimism and depression is linear and contains the following two points: (1, 7) and (4, 3). It can be represented by the line y = mx + b, where m is the slope, and b is the y-intercept.

Begin this discussion by: Find the slope of the line between the two points you have been given above. Find the y-intercept of the line between the two points you have been given above. Write the equation representing the relationship between optimism and depression using your determined slope and y-intercept. Write down a level of depression to the nearest tenth (between 1 and 4) and a level of optimism to the nearest tenth (between 1 and 8) and clearly label each (these will be used with your responses to classmates).

Next, respond to two peers in the following way:

Response 1: Using the level of depression a classmate shared with your equation, solve for their level of optimism.

Classmate1– Slope: 7-3/1-4 = 4/-3 Finding B: 7=-4/3(1) + B 7=-1 1/3+B add 1 1/3 8 1/3 = B Y intercept: 8 1/3 Equation: (4,3) 3=(-4/3)(4)+ 8 1/3 3=3 Write down a level of depression to the nearest tenth (between 1 and 4) and a level of optimism to the nearest tenth (between 1 and 8) and clearly label each (these will be used with your responses to classmates). Depression: 3.8 Optimism: 7.7

Response 2: Using the level of optimism that a different classmate shared with your equation, solve for their level of depression.

Classmate 2

Slope= -4/3 Find B y=-4/3x+B 7=-4/3(1)+B 7+-1 1-/3+B 7+1 1/3=B 8 1/3= B Equation Y=-4/3x+8 1/3 7=-4/2(1)+8 1/3 7=-1 1/3+ 8 1/3 7=7 X-axis depression=3.3 Y-axis optimism=6.5