Use the function y = 3/2x + 3 to complete the table of values.
Understand the Problem
The question is asking to use the given linear function to calculate corresponding y-values for specified x-values in a table.
Answer
The completed values are: \( y(4) = 9, y(8) = 15, y(0) = 3, y(-3) = -1.5 \).
Answer for screen readers
The completed table of values is:
| ( x ) | ( y ) |
|---|---|
| 4 | 9 |
| 8 | 15 |
| 0 | 3 |
| -3 | -1.5 |
Steps to Solve
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Identify the Function The linear function provided is given as ( y = \frac{3}{2}x + 3 ).
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Calculate ( y ) for ( x = 4 ) Substitute ( x = 4 ) into the function: $$ y = \frac{3}{2}(4) + 3 $$ Calculating gives: $$ y = 6 + 3 = 9 $$
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Calculate ( y ) for ( x = 8 ) Now, substitute ( x = 8 ) into the function: $$ y = \frac{3}{2}(8) + 3 $$ Calculating gives: $$ y = 12 + 3 = 15 $$
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Calculate ( y ) for ( x = 0 ) Now, substitute ( x = 0 ) into the function: $$ y = \frac{3}{2}(0) + 3 $$ Calculating gives: $$ y = 0 + 3 = 3 $$
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Calculate ( y ) for ( x = -3 ) Lastly, substitute ( x = -3 ) into the function: $$ y = \frac{3}{2}(-3) + 3 $$ Calculating gives: $$ y = -\frac{9}{2} + 3 = -4.5 + 3 = -1.5 $$
The completed table of values is:
| ( x ) | ( y ) |
|---|---|
| 4 | 9 |
| 8 | 15 |
| 0 | 3 |
| -3 | -1.5 |
More Information
This function is a linear equation, where the slope is ( \frac{3}{2} ), which means for every 2 units you move right along the x-axis, you move 3 units up on the y-axis.
Tips
- Forgetting to substitute the x-value into the function correctly.
- Making arithmetic mistakes when multiplying or adding.
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