Answer:
To determine the value of p when q = 65, we need to find the relationship between p and q based on the given information.
From the given information, we know that when q = 20, p = 5. This suggests that there is a linear relationship between p and q.
To find the equation for this linear relationship, we can use the concept of slope-intercept form: y = mx + b, where y is p, x is q, m is the slope, and b is the y-intercept.
Given that q = 20 corresponds to p = 5, we can substitute these values into the equation to solve for the y-intercept:
5 = m * 20 + b
Simplifying the equation:
5 = 20m + b
Now, let's find the value of m, the slope, using the given information that q = 20 corresponds to p = 5:
m = (p2 - p1) / (q2 - q1)
m = (5 - 0) / (20 - 0)
m = 5/20
m = 1/4
Now, we have the slope (m = 1/4) and the y-intercept (b = 5). We can substitute these values into the equation y = mx + b:
p = (1/4)q + 5
To find the value of p when q = 65, we substitute q = 65 into the equation:
p = (1/4)(65) + 5
p = 65/4 + 5
p = 16.25 + 5
p = 21.25
Therefore, when q = 65, the value of p is 21.25.