(a) Copy and complete the table of value
shown below for the equation
.

Question

(a) Copy and complete the table of value shown below for the equation $$ y=4 x-2 $$.

UpStudy AI · Accepted Answer

Certainly! Let's create and complete a table of values for the linear equation $$ y = 4x - 2 $$. This table will show corresponding $$ y $$ values for selected $$ x $$ values.

### (a) Table of Values for $$ y = 4x - 2 $$

| $$ x $$ | $$ y = 4x - 2 $$ |
|:-------:|:---------------:|
|  -3     | $$ 4(-3) - 2 = -12 - 2 = -14 $$ |
|  -2     | $$ 4(-2) - 2 = -8 - 2 = -10 $$  |
|  -1     | $$ 4(-1) - 2 = -4 - 2 = -6 $$   |
|   0     | $$ 4(0)  - 2 = 0  - 2 = -2 $$    |
|   1     | $$ 4(1)  - 2 = 4  - 2 = 2 $$     |
|   2     | $$ 4(2)  - 2 = 8  - 2 = 6 $$     |
|   3     | $$ 4(3)  - 2 = 12 - 2 = 10 $$    |

### Explanation:

1. **Choose $$ x $$-values:** Select a range of $$ x $$-values for which you want to find the corresponding $$ y $$-values. In this case, we've chosen $$ x = -3, -2, -1, 0, 1, 2, 3 $$.

2. **Apply the equation:** For each $$ x $$-value, substitute it into the equation $$ y = 4x - 2 $$ to compute $$ y $$.
   
   - **Example Calculation for $$ x = 2 $$:**
     $$
     y = 4(2) - 2 = 8 - 2 = 6
     $$

3. **Complete the table:** Fill in each row with the corresponding $$ y $$-value calculated from the equation.

### Visual Representation:

Here's how the table looks with all values filled in:

| $$ x $$ | $$ y $$ |
|:-------:|:-------:|
|  -3     |  -14    |
|  -2     |  -10    |
|  -1     |   -6    |
|   0     |   -2    |
|   1     |    2    |
|   2     |    6    |
|   3     |   10    |

### Plotting the Points (Optional)

If you plot these points on a coordinate plane, you'll notice they form a straight line, which is characteristic of linear equations. The slope of the line is 4, and the y-intercept is -2.

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Feel free to choose different $$ x $$-values to explore how $$ y $$ changes accordingly!
Here is the completed table of values for the equation $$ y = 4x - 2 $$: | $$ x $$ | $$ y $$ | |:-------:|:-------:| | -3 | -14 | | -2 | -10 | | -1 | -6 | | 0 | -2 | | 1 | 2 | | 2 | 6 | | 3 | 10 |

(a) Copy and complete the table of value
shown below for the equation
.

Upstudy AI Solution

Answer

Solution

Mind Expander

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(a) Copy and complete the table of value shown below for the equation .

Upstudy AI Solution

Answer

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(a) Copy and complete the table of value
shown below for the equation
.