A) ON SEPARATE GRAPHS ( THE CARTESIAN PLANE), DRAW THE FOLLOWING STRAIGHT LINES USING THE GIVEN DOMAINS. I) $$ \mathrm{y}=\mathrm{x}+7 $$ for $$ \{x:-3 \leq x \leq 3\} $$ II) $$ 3 \mathrm{y}+6 \mathrm{x}=12 $$ for $$ \{x:-1 \leq x \leq 4\} $$ III) $$ \mathrm{y}=\mathrm{x} $$ for $$ \{x:-3 \leq x \leq 3\} $$ IV) $$ \mathrm{y}=5 \mathrm{x} $$ for $$ \{x:-2 \leq x \leq 2\} $$

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To graph the given lines on separate Cartesian planes, we will first determine the points that correspond to the specified domains for each equation.

### I) $$ y = x + 7 $$ for $$ \{-3 \leq x \leq 3\} $$

1. Calculate the y-values for the endpoints of the domain:
   - For $$ x = -3 $$: 
     $$
     y = -3 + 7 = 4
     $$
   - For $$ x = 3 $$: 
     $$
     y = 3 + 7 = 10
     $$

2. The points to plot are:
   - $$ (-3, 4) $$
   - $$ (3, 10) $$

3. Draw a straight line connecting these two points.

### II) $$ 3y + 6x = 12 $$ for $$ \{-1 \leq x \leq 4\} $$

1. Rearrange the equation to solve for $$ y $$:
   $$
   3y = 12 - 6x \implies y = 4 - 2x
   $$

2. Calculate the y-values for the endpoints of the domain:
   - For $$ x = -1 $$: 
     $$
     y = 4 - 2(-1) = 4 + 2 = 6
     $$
   - For $$ x = 4 $$: 
     $$
     y = 4 - 2(4) = 4 - 8 = -4
     $$

3. The points to plot are:
   - $$ (-1, 6) $$
   - $$ (4, -4) $$

4. Draw a straight line connecting these two points.

### III) $$ y = x $$ for $$ \{-3 \leq x \leq 3\} $$

1. Calculate the y-values for the endpoints of the domain:
   - For $$ x = -3 $$: 
     $$
     y = -3
     $$
   - For $$ x = 3 $$: 
     $$
     y = 3
     $$

2. The points to plot are:
   - $$ (-3, -3) $$
   - $$ (3, 3) $$

3. Draw a straight line connecting these two points.

### IV) $$ y = 5x $$ for $$ \{-2 \leq x \leq 2\} $$

1. Calculate the y-values for the endpoints of the domain:
   - For $$ x = -2 $$: 
     $$
     y = 5(-2) = -10
     $$
   - For $$ x = 2 $$: 
     $$
     y = 5(2) = 10
     $$

2. The points to plot are:
   - $$ (-2, -10) $$
   - $$ (2, 10) $$

3. Draw a straight line connecting these two points.

### Summary of Points to Plot

- **Graph I**: Points $$ (-3, 4) $$ and $$ (3, 10) $$
- **Graph II**: Points $$ (-1, 6) $$ and $$ (4, -4) $$
- **Graph III**: Points $$ (-3, -3) $$ and $$ (3, 3) $$
- **Graph IV**: Points $$ (-2, -10) $$ and $$ (2, 10) $$

You can now plot these points on separate Cartesian graphs and draw the lines accordingly.
To graph the lines, calculate the y-values for the given x-ranges, plot the points, and draw the lines connecting them.

A) ON SEPARATE GRAPHS ( THE
CARTESIAN PLANE), DRAW THE
FOLLOWING
STRAIGHT LINES USING THE GIVEN
DOMAINS.
I) for
II) for
III) for
IV) for

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A) ON SEPARATE GRAPHS ( THE CARTESIAN PLANE), DRAW THE FOLLOWING STRAIGHT LINES USING THE GIVEN DOMAINS. I) for II) for III) for IV) for

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Answer

Solution

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Latest Algebra Questions

A) ON SEPARATE GRAPHS ( THE
CARTESIAN PLANE), DRAW THE
FOLLOWING
STRAIGHT LINES USING THE GIVEN
DOMAINS.
I) for
II) for
III) for
IV) for