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{(–3, –13), (0, –7), (3, –1), (6, 5)} make an equation

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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

User TheScholar
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