Final answer:
The ordered points lie on a line and can be represented by the linear equation y = 2x - 7, which is determined by calculating the consistent slope of 2 using the given points and then finding the y-intercept to be -7.
Step-by-step explanation:
To create an equation from the set of ordered pairs {(−3, −13), (0, −7), (3, −1), (6, 5)}, we need to determine if these points lie on a line.
If they do, then they will satisfy a linear equation of the form y = mx + b, where m is the slope and b is the y-intercept.
First, calculate the slope (m) using any two points:
m = (y2 − y1) / (x2 − x1)
For example, using the points (0, −7) and (3, −1), we get:
m = (−1 − (−7)) / (3 − 0)
= 6 / 3
= 2
This slope should be consistent for all pairs of points if they indeed define a line.
Next, we use the slope and one point to find b, the y-intercept.
Substitute x = 0 and y = −7 into the equation:
−7 = 2(0) + b
Simplifying, we find that b = −7. Therefore, the equation that represents the set of points is:
y = 2x − 7