The equation representing the relationship is:y=−6.5x−58.5
To identify the constant in the relationship between the ordered pairs, let's look at the differences in the y-values (second coordinates). The constant is the common difference between these y-values.
For the given ordered pairs {(-8, -6.5), (-4, -13), (-2, -26)}, we can find the constant by subtracting the y-values:
−13−(−6.5)=−13+6.5=−6.5
−26−(−13)=−26+13=−13
So, the constant is -6.5.
Now, to write an equation to represent the relationship, we can use the slope-intercept form of a linear equation:
y=mx+b, where
m is the slope and
b is the y-intercept.
We already know the constant (m) is -6.5. Now, let's use one of the points to find the y-intercept (b). Let's use the point (-8, -6.5):
−6.5=−6.5×(−8)+b
Now, solve for b:
−6.5=52+b
b=−58.5
So, the equation representing the relationship is:y=−6.5x−58.5