Question

which equations represents the number of squares in any given figure? (use the image below to help guide you)
figure 1
figure 2
figure 3
\\( \bigcirc \\) \\( s = f + 2 \\)
\\( \bigcirc \\) \\( f = s + 2 \\)
\\( \bigcirc \\) \\( s = 2f + 1 \\)
\\( \bigcirc \\) \\( f = 2s + 1 \\)
identify the value of y - intercept from the equation 3y - x

Explanation:

Step1: Count squares in each figure

Figure 1 (f=1): Squares \( s = 3 \)
Figure 2 (f=2): Squares \( s = 5 \)
Figure 3 (f=3): Squares \( s = 7 \)

Step2: Test each equation

• \( s = f + 2 \): For f=1, \( 1 + 2 = 3 \) (matches). For f=2, \( 2 + 2 = 4 \) (does not match s=5).
• \( f = s + 2 \): For s=3, \( 3 + 2 = 5

eq 1 \) (no).

• \( s = 2f + 1 \): For f=1, \( 2(1) + 1 = 3 \) (matches). For f=2, \( 2(2) + 1 = 5 \) (matches). For f=3, \( 2(3) + 1 = 7 \) (matches).
• \( f = 2s + 1 \): For s=3, \( 2(3) + 1 = 7

eq 1 \) (no).

Answer:

\( s = 2f + 1 \)