Understanding First Differences and Linear Equations

What is the primary purpose of using first differences in a set of coordinates?

• To calculate the slope of the line

• To find the midpoint of the coordinates

• To check if the coordinates plot a straight line

• To determine if the coordinates form a circle

Why is it important for x-values to be evenly spaced when calculating first differences?

• It helps in plotting the graph accurately

• It simplifies the calculation of y-values

• It ensures the differences are constant

• It allows for easier subtraction of y-values

What does a constant first difference indicate about a set of coordinates?

• The coordinates are randomly distributed

• The coordinates form a quadratic equation

• The coordinates form a cubic equation

• The coordinates plot a linear equation

In the example provided, what was the first difference calculated for the second set of y-values?

• Two

• Five

• Four

• Three

What conclusion can be drawn if all first differences in a table are the same?

• The table represents a non-linear equation

• The table suggests a linear equation

• The table is incomplete

• The table needs more data points