Question

in the rows below, type as many linear equations as you need to collect all the stars.

Explanation:

Step1: Count the number of stars

Looking at the image, we can see that there are 4 stars (one on the left, two in the middle, one on the right). Wait, let's check again. Wait, the stars: let's list them. First row (middle vertical): 1 star. Second row (horizontal): left star, right star. Third row (middle vertical): 1 star. Wait, no, let's count again. Wait, the visible stars: let's see, the yellow stars. Let's count: 1 (top middle), 1 (left middle), 1 (right middle), 1 (bottom middle). So total of 4 stars? Wait, no, maybe I miscounted. Wait, the image shows: let's see, the stars are at different positions. Let's count each star:

• Star 1: left side (middle horizontal)
• Star 2: top middle (vertical)
• Star 3: right side (middle horizontal)
• Star 4: bottom middle (vertical)

So that's 4 stars. Wait, but maybe the problem is to write linear equations to collect all stars. Wait, maybe the positions are on a number line? The numbers at the top are 4, 8, 12, 16, 20? Wait, no, the horizontal line has numbers 4, 8, 12, 16, 20? Wait, maybe the x - axis is labeled with those numbers. Let's assume the positions:

• Left star: let's say at x = 4 (since 4 is the first number)
• Top middle star: maybe at x = 8?
• Right middle star: at x = 16?
• Bottom middle star: at x = 12?

Wait, maybe the linear equations are of the form x = a, where a is the position of the star. So for each star, we can write x = 4, x = 8, x = 12, x = 16. But maybe the problem is to collect all stars, so we need to write equations that pass through the stars. Since they are on a horizontal or vertical line? Wait, the stars seem to be on different vertical and horizontal lines. Wait, maybe the linear equations are vertical lines (x = constant) or horizontal lines (y = constant). Let's assume the y - coordinates: maybe the left star is at (4, y1), top middle at (8, y2), right middle at (16, y3), bottom middle at (12, y4). But maybe the problem is simpler, like counting the number of stars and writing equations to represent their positions. Wait, maybe the answer is that there are 4 stars, and the linear equations are x = 4, x = 8, x = 12, x = 16 (assuming each star is on a vertical line with those x - coordinates).

Wait, maybe I misinterpret the problem. The problem says "type as many linear equations as you need to collect all the stars". So each linear equation represents a line that passes through one or more stars. Let's look at the positions:

• Left star: let's say its x - coordinate is 4 (from the number line at the top: 4, 8, 12, 16, 20)
• Top middle star: x = 8
• Bottom middle star: x = 12
• Right middle star: x = 16

So these are vertical lines (since x is constant, y can be any). So the linear equations are x = 4, x = 8, x = 12, x = 16.

Step2: Confirm the count

Counting the stars: 1 (x = 4), 1 (x = 8), 1 (x = 12), 1 (x = 16). So four stars, four linear equations (vertical lines) to collect each star.

Answer:

The linear equations to collect all stars are \( x = 4 \), \( x = 8 \), \( x = 12 \), \( x = 16 \) (assuming the stars are at these x - coordinates on a horizontal number line). The number of stars is 4.