Question

select the correct answer

x	y
3	15
7	31
10	43

which of the following linear equations corresponds to the table above?

a. $y = 4x - 3$

b. $y = \frac{5}{3}x + 3$

c. $y = \frac{3}{5}x + 3$

d. $y = 4x + 3$

Explanation:

Step1: Test x=0 in each equation

• For A: \( y = 4(0)-3=-3

eq 3 \)

• For B: \( y=\frac{5}{3}(0)+3 = 3 \)
• For C: \( y=\frac{3}{5}(0)+3 = 3 \)
• For D: \( y = 4(0)+3=3 \)

Step2: Test x=3 in remaining equations (B, C, D)

• For B: \( y=\frac{5}{3}(3)+3=5 + 3=8

eq15 \)

• For C: \( y=\frac{3}{5}(3)+3=\frac{9}{5}+3=\frac{24}{5}

eq15 \)

• For D: \( y = 4(3)+3=12 + 3=15 \)

Step3: Verify x=7 and x=10 for D

• x=7: \( y = 4(7)+3=28 + 3=31 \) (matches table)
• x=10: \( y = 4(10)+3=40 + 3=43 \) (matches table)

Answer:

D. \( y = 4x + 3 \)