Final answer:
The linear equation that represents the ordered pairs {(2,3), (3,5), (4,7), (5,9)} is y = 2x - 1, where the slope is 2 and the y-intercept is -1.
Step-by-step explanation:
To write an equation for the set of ordered pairs {(2,3), (3,5), (4,7), (5,9)}, we need to determine if the relationship between the x-values (the first number in each pair) and the y-values (the second number in each pair) forms a linear pattern. Observing the pattern, we can see that for each increase of 1 in the x-value, the y-value increases by 2. This suggests a linear relationship with a slope (m) of 2.
The general form of a linear equation is y = mx + b, where m is the slope and b is the y-intercept. The y-intercept is the point where the line crosses the y-axis (where x=0). To find it, we can plug in one of the given pairs into the equation and solve for b. Using the pair (2,3), we substitute and get 3 = 2(2) + b, which simplifies to b = -1.
Therefore, the linear equation that represents the given ordered pairs is y = 2x - 1.