To find the value of C, we can use the formula for the gradient (slope) of a line, which is the change in y divided by the change in x between two points on the line. In this case, the points are A(5, -C²) and B(C, -3).
The gradient (m) is given by:
m = (change in y) / (change in x)
Let's calculate the change in y and the change in x:
Change in y = y₂ - y₁
= (-3) - (-C²)
= -3 + C²
Change in x = x₂ - x₁
= C - 5
Now, using the gradient formula:
C = (change in y) / (change in x)
= (-3 + C²) / (C - 5)
We can solve this equation for C. Multiplying both sides by (C - 5) gives:
C(C - 5) = -3 + C²
C² - 5C = -3 + C²
-5C = -3
C = -3 / -5
C = 3/5
Therefore, the value of C is 3/5.