Questions: Match each equation to one of its solutions. Hint: - Substitute the x-value of 3 into each equation to find the corresponding y value. OR * Use the DESMOS calculator in Graphing Mode to help you graph. Look on each graph for when the x-value is 3. y=1/3(5x-6) a. (3,27.5) y=1.3(2)^x b. (3,10.4) y=100(0.7)^x c. (3,34.3) y=-5/6 x+30 d. (3,3)

Solution Steps

To match each equation to its solution, substitute \( x = 3 \) into each equation and calculate the corresponding \( y \)-value. Then, compare the calculated \( y \)-values with the given options.

1. For \( y = \frac{1}{3}(5x - 6) \): \[ y = \frac{1}{3}(5 \times 3 - 6) = \frac{1}{3}(15 - 6) = \frac{1}{3} \times 9 = 3 \]

2. For \( y = 1.3(2)^x \): \[ y = 1.3 \times 2^3 = 1.3 \times 8 = 10.4 \]

3. For \( y = 100(0.7)^x \): \[ y = 100 \times 0.7^3 = 100 \times 0.343 = 34.3 \]

4. For \( y = -\frac{5}{6}x + 30 \): \[ y = -\frac{5}{6} \times 3 + 30 = -\frac{15}{6} + 30 = -2.5 + 30 = 27.5 \]

• Equation \( y = \frac{1}{3}(5x - 6) \) gives \( y = 3 \), matching option \( (3, 3) \).
• Equation \( y = 1.3(2)^x \) gives \( y = 10.4 \), matching option \( (3, 10.4) \).
• Equation \( y = 100(0.7)^x \) gives \( y = 34.3 \), matching option \( (3, 34.3) \).
• Equation \( y = -\frac{5}{6}x + 30 \) gives \( y = 27.5 \), matching option \( (3, 27.5) \).

Final Answer