Look for a pattern in the table. Then write an equation that represents the table.
x 0 1 2 3
y 1.5 4 6.5 9
To look for a pattern in the table, we can observe the relationship between the values of x and y.
If we examine the differences between consecutive x-values and y-values, we can see that the differences for both x and y are increasing by 2 each time.
x: 1 - 0 = 1, 2 - 1 = 1, 3 - 2 = 1
y: 4 - 1.5 = 2.5, 6.5 - 4 = 2.5, 9 - 6.5 = 2.5
Based on this pattern, we can conclude that the equation representing the table is a linear function with a constant rate of change.
The equation can be written in the general form of a linear equation, y = mx + b, where m represents the slope (rate of change) and b represents the y-intercept.
To find the slope, we can take any two points from the table and calculate the difference in y-values divided by the difference in x-values:
m = (y2 - y1) / (x2 - x1)
Using the points (0, 1.5) and (1, 4):
m = (4 - 1.5) / (1 - 0) = 2.5 / 1 = 2.5
So, the slope of the equation is 2.5.
Now, we need to find the y-intercept (b). We can substitute the values of any point from the table and the slope (m) into the equation and solve for b.
Let's use the point (0, 1.5):
1.5 = 2.5(0) + b
1.5 = b
The y-intercept (b) is 1.5.
Putting it all together, the equation that represents the table is:
y = 2.5x + 1.5