Use the function y = (3/2)x + 3 to complete the table of values.
Understand the Problem
The question is asking us to use the given function to calculate corresponding y-values for a provided x-value table. This involves substituting the x-values into the function and solving for y.
Answer
The completed values are: $y = 9, 15, 3, 0$ for $x = 4, 8, 0, -2$.
Answer for screen readers
The completed table of values is:
| x | 4 | 8 | 0 | -2 |
|---|---|---|---|---|
| y | 9 | 15 | 3 | 0 |
Steps to Solve
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Identify the function We are given the function ( y = \frac{3}{2}x + 3 ).
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Substitute x value 4 Plug in ( x = 4 ) into the function: $$ y = \frac{3}{2}(4) + 3 $$ Calculating this gives: $$ y = 6 + 3 = 9 $$
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Substitute x value 8 Now, use ( x = 8 ): $$ y = \frac{3}{2}(8) + 3 $$ Calculating this gives: $$ y = 12 + 3 = 15 $$
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Substitute x value 0 Next, use ( x = 0 ): $$ y = \frac{3}{2}(0) + 3 $$ Calculating this gives: $$ y = 0 + 3 = 3 $$
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Substitute x value -2 Finally, use ( x = -2 ): $$ y = \frac{3}{2}(-2) + 3 $$ Calculating this gives: $$ y = -3 + 3 = 0 $$
The completed table of values is:
| x | 4 | 8 | 0 | -2 |
|---|---|---|---|---|
| y | 9 | 15 | 3 | 0 |
More Information
The function ( y = \frac{3}{2}x + 3 ) is a linear equation. It means for every unit increase in ( x ), ( y ) increases by ( \frac{3}{2} ) units.
Tips
- Forgetting to multiply correctly when substituting values into the function.
- Incorrectly simplifying or adding numbers. Avoid these by double-checking calculations step by step.
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