Jill created a pattern where the equation for the number of shapes was y = 5x - 1. Describe what Jill's pattern could look like.
Jill's pattern could look like a sequence of shapes, where the number of shapes (y) depends on the position (x) in the sequence. The equation y = 5x - 1 indicates that for each position in the sequence, the number of shapes is calculated by multiplying the position number by 5 and then subtracting 1.
For example, when x = 1, the equation becomes y = 5(1) - 1, which results in y = 4. This means there may be 4 shapes in the pattern at position 1.
Similarly, if x = 2, the equation becomes y = 5(2) - 1, resulting in y = 9. This implies that there may be 9 shapes in the pattern at position 2.
Thus, Jill's pattern could have different numbers of shapes for each position, all following the equation y = 5x - 1.
Jill's pattern can be described graphically by plotting points on a coordinate plane using the equation y = 5x - 1.
To do this, you can choose different values for x to find corresponding values for y. Let's choose a few values:
When x = 0, y = 5(0) - 1 = -1. So, we have the point (0, -1).
When x = 1, y = 5(1) - 1 = 5 - 1 = 4. So, we have the point (1, 4).
When x = 2, y = 5(2) - 1 = 10 - 1 = 9. So, we have the point (2, 9).
When x = 3, y = 5(3) - 1 = 15 - 1 = 14. So, we have the point (3, 14).
When x = 4, y = 5(4) - 1 = 20 - 1 = 19. So, we have the point (4, 19).
Now, plot these points on a graph and connect them to see the pattern.
The graph will show a straight line with a positive slope. Each point represents a value of x and the corresponding value of y. As x increases, y also increases following the equation y = 5x - 1. The pattern shows a linear relationship where y is dependent on x, and for every increase of x by 1, y increases by 5.